Prime Time
Master the atomic building blocks of numbers! Explore factors, multiples, prime & composite classifications, co-prime safekeeping secrets, the Sieve of Eratosthenes, unique prime factorisation trees, and lightning-fast divisibility tests for 2, 4, 5, 8, and 10.
What is Class 6 Maths Chapter 5: Prime Time?
A factor divides a number completely (e.g., factors of 12 are 1, 2, 3, 4, 6, 12). A multiple is obtained by multiplying (e.g., multiples of 3 are 3, 6, 9, 12...).
A prime number has exactly two factors (1 and itself). A composite number has >2 factors. 1 is neither prime nor composite; 2 is the only even prime.
Two numbers are co-prime if their only common factor is 1 (HCF = 1). In Thread Art on a circle of N pins, jumping by G pins visits every pin if and only if HCF(N, G) = 1.
Divisible by 2 if last digit is even; by 4 if last 2 digits divide by 4; by 5 if last digit is 0 or 5; by 8 if last 3 digits divide by 8; by 10 if last digit is 0.
What You Will Learn in Chapter 5
Common Multiples & Factors
Jump Jackpot game, Idli-Vada game, finding common factor sets, and the first common multiple.
Prime & Composite Numbers
Rectangular arrays (12 vs 7 figs), 25 primes up to 100, Sieve of Eratosthenes, and twin prime pairs.
Co-Prime Numbers & Thread Art
Safekeeping treasure vault codes, disjoint factor sets, and circular string polygon theorems.
Prime Factorisation Trees
Branching factor trees for 56, 36, 72, 80; uniqueness of prime factors (Fundamental Theorem).
Divisibility Tests (2, 4, 5, 8, 10)
Place-value logic behind divisibility rules, remainder patterns, and leap year calendar math.
Fun with Numbers & Prime Puzzles
4-box number deduction (9, 16, 25, 43) and 3x3 prime multiplication matrix puzzles.
Interactive Chapter Roadmap & Quick Jumps
Common Multiples and Common Factors
Activity 1: The Idli-Vada Game
Students count numbers in sequence from 1 to 60. When a number is a multiple of 3, they shout "Idli!". When it is a multiple of 5, they shout "Vada!". When it is a multiple of both 3 and 5, they shout "Idli-Vada!".
Multiples of 3 (Idli): 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
Multiples of 5 (Vada): 5, 10, 15, 20, 25, 30, 35, 40, 45...
Common Multiples (Idli-Vada!): 15, 30, 45, 60...
The first number where both actions coincide is 15 (First Common Multiple / LCM).
Activity 2: Jump Jackpot & Factors
A factor (or divisor) of a number divides it exactly with zero remainder. For instance, in the Jump Jackpot game on numbers 1 to 50, jumps of step 4 step on 4, 8, 12, 16... and jumps of step 6 step on 6, 12, 18, 24...
Factors of 14: 1, 2, 7, 14
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common Factors of 14 and 36: 1 and 2
The highest common factor is 2 (HCF).
Interactive Multiples & Factors Explorer
Prime and Composite Numbers
Prime Numbers
Whole numbers greater than 1 with exactly two distinct factors (1 and itself).
Arranging 7 figs can only form a 1×7 line.
Composite Numbers
Whole numbers greater than 1 with more than two factors (at least one extra divisor).
Arranging 12 figs can form 1×12, 2×6, or 3×4 grids.
Crucial Number Facts
- 1 is neither: has only 1 factor (1).
- 2 is unique: only even prime.
- Twin Primes: differ by 2: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73).
- 7 Consecutive Composites: 90, 91, 92, 93, 94, 95, 96.
Interactive Sieve of Eratosthenes (1–100 Grid)
Step through Eratosthenes' 2,200-year-old algorithm to sieve out composites and reveal all 25 primes!
Co-Prime Numbers for Safekeeping Treasures
The Co-Prime Vault Secret
Two whole numbers are called co-prime (or mutually prime) if their only common factor is 1 (HCF = 1).
Example: 4 and 9
Factors of 4 = {1, 2, 4}
Factors of 9 = {1, 3, 9}
Only common factor = 1 → 4 and 9 are CO-PRIME!
LCM(a, b) = a × b.Thread Art (Kolam & String Math)
Arrange N equally spaced pins on a circle and wind thread by jumping G pins each time.
The Golden Theorem of Thread Art:
The thread will visit every single pin in a single unbroken loop if and only if the number of pins N and the jump gap G are co-prime (HCF(N, G) = 1).
If HCF(N, G) = d > 1, the thread closes into a smaller polygon visiting only N/d pins.
Interactive Co-Prime Tester
HCF = 1. Product = LCM = 120.
Thread Art Geometry Predictor
Visits ALL 12 pins in 1 unbroken loop (Complete pattern)!
Prime Factorisation and Factor Trees
The Fundamental Theorem of Arithmetic
Every composite number can be broken down into a product of prime numbers. Except for the order of factors, this prime representation is completely unique.
56 = 2 × 2 × 2 × 7 = 2³ × 7
36 = 2 × 2 × 3 × 3 = 2² × 3²
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
80 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5
Applications of Prime Factorisation
- 1. Checking Co-Primes: If two numbers share NO common prime factors in their prime factorisations, they are guaranteed to be co-prime.
- 2. Checking Divisibility: Number A is divisible by number B if and only if all prime factors of B are contained inside A with equal or greater powers.
Interactive Prime Factor Tree Explorer
Enter any number (up to 1,000) to see its prime building blocks!
Divisibility Tests for 2, 4, 5, 8, and 10
10 is divisible by 2, so only unit digit matters.
100 is divisible by 4 (4×25), so only tens and units matter.
10 is divisible by 5 (5×2), so only unit digit matters.
1000 is divisible by 8 (8×125), so only last 3 digits matter.
Multiples of 10 always end in 0.
Instant Divisibility Inspector
Type any number to test divisibility for 2, 4, 5, 8, and 10 simultaneously!
Fun with Numbers and Prime Puzzles
The 4-Box Deduction Game (9, 16, 25, 43)
Can you explain what makes each of these four numbers mathematically unique compared to the other three?
Only single-digit number & only multiple of 3.
Only even number in the group & multiple of 4/8.
Only multiple of 5 & ends in digit 5.
Only prime number (9, 16, 25 are all square composites).
The 3x3 Prime Product Puzzle Matrix
Fill each cell with prime numbers such that row and column products match the given targets!
All 9 entries are prime numbers satisfying 2×5×3=30, 7×2×5=70, 3×5×7=105, 2×7×3=42, 5×2×5=50, and 3×5×7=105!
Prime Time – Worked Examples
Example 1: Finding All Factors of 48
Question: Find all the factors of 48 by writing it as products of pairs of numbers.
How to Think: Systematically test integers starting from 1 up to √48 ≈ 6.9.
1 × 48 = 48
2 × 24 = 48
3 × 16 = 48
4 × 12 = 48
6 × 8 = 48
Answer: The complete set of factors of 48 is: {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.
Example 2: Finding Common Factors of 20 and 28
Question: Determine the common factors of 20 and 28 and find their highest common factor (HCF).
How to Think: List all factors of each number, then find their intersection.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 28: 1, 2, 4, 7, 14, 28
Intersection of factors: {1, 2, 4}
Answer: The common factors are 1, 2, and 4. The Highest Common Factor (HCF) is 4.
Example 3: Prime Factorisation of 120
Question: Construct a factor tree and write down the prime factorisation of 120 in exponential form.
How to Think: Repeatedly divide by the smallest prime factor.
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 is prime.
Answer: 120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5.
Example 4: Testing Co-Primes using Prime Factors
Question: Check whether 35 and 44 are co-prime without listing all factors.
How to Think: Find the prime factors of both numbers and check if they share any primes.
Prime factorisation of 35: 5 × 7
Prime factorisation of 44: 2 × 2 × 11 = 2² × 11
Shared prime factors: None!
Answer: Since they share no common prime factors, their HCF is 1, proving that 35 and 44 are co-prime.
Example 5: Divisibility by 4 and 8 for a 6-digit Number
Question: Test if the number 925,328 is divisible by 4 and by 8 without performing long division.
How to Think: Check the last 2 digits for 4, and the last 3 digits for 8.
Last 2 digits: 28. Since 28 ÷ 4 = 7 (remainder 0), 925,328 is divisible by 4.
Last 3 digits: 328. 328 ÷ 8 = 41 (remainder 0).
Answer: 925,328 is divisible by BOTH 4 and 8.
Example 6: Divisibility by 5 and 10
Question: Is 48,295 divisible by 5? Is it divisible by 10? Explain using unit digit rules.
How to Think: Check the unit digit: it is 5.
Divisibility by 5 requires unit digit 0 or 5. Here unit digit is 5, so it IS divisible by 5.
Divisibility by 10 requires unit digit 0. Since unit digit is 5, it is NOT divisible by 10.
Answer: 48,295 is divisible by 5, but NOT divisible by 10.
Example 7: Next Leap Year Calculation
Question: A student notes that 2024 is a leap year. Which of the next three election years—2029, 2032, or 2035—will be a leap year?
How to Think: Test if the last two digits of each year form a multiple of 4.
2029: Last 2 digits = 29 (29 ÷ 4 = 7 r 1) → Not a leap year.
2032: Last 2 digits = 32 (32 ÷ 4 = 8 r 0) → LEAP YEAR!
2035: Last 2 digits = 35 (35 ÷ 4 = 8 r 3) → Not a leap year.
Answer: Only the year 2032 will be a leap year.
Example 8: Thread Art Star on 16 Pins
Question: On a circular board with 16 pins, what will happen if we wind thread with a step gap of G = 6 versus G = 5?
How to Think: Compute HCF(16, G).
For G = 6: HCF(16, 6) = 2. Number of pins visited = 16 ÷ 2 = 8 pins (closes into an octagon).
For G = 5: HCF(16, 5) = 1. Number of pins visited = 16 ÷ 1 = 16 pins (visits all 16 pins!).
Answer: A gap of 6 only visits 8 pins, whereas a gap of 5 visits all 16 pins creating a complete star design.
15 Interactive Practice Questions
What are all the factors of 36?
What is the first common multiple of 4 and 6?
Which of the following numbers is a prime number?
Which number is the ONLY even prime number?
Which of the following pairs represents twin primes?
Which pair of numbers is co-prime?
What is the prime factorisation of 56?
A 4-digit number 7,43_ is divisible by 4. What digits can fill the blank?
Which of the following numbers is divisible by 8?
How many prime numbers exist between 1 and 100?
Why is 1 classified as NEITHER prime nor composite?
In Thread Art with 12 pins, which jump step G will connect all 12 pins in a single path?
What are the 7 consecutive composite numbers under 100?
If a number is divisible by both 4 and 5, it must ALWAYS be divisible by:
Which of the following years is a Leap Year?
12 Challenge & Figure It Out Questions
The Jump Jackpot Strategy (Section 5.1)
In the Jump Jackpot game on numbers 1 to 50, Player A jumps by 4s and Player B jumps by 6s. Which tiles between 1 and 50 will BOTH players step on? What is their first common jackpot tile?
The Idli-Vada Game Pattern (Section 5.1)
Students sit in a circle counting from 1 to 60. For multiples of 3 they shout 'Idli!', for multiples of 5 they shout 'Vada!', and for multiples of both they shout 'Idli-Vada!'. Which counts trigger 'Idli-Vada!'?
Rectangular Arrangements: 12 vs 7 Figs (Section 5.2)
A fruit vendor wants to arrange fresh figs into complete rectangular arrays with no figs left over. How many different rectangular grid shapes can be formed with 12 figs versus 7 figs? Explain using prime/composite theory.
Sieve Elimination Logic for Primes up to 100 (Section 5.2)
Why is it sufficient to cross out multiples of only 2, 3, 5, and 7 when using the Sieve of Eratosthenes to find all primes up to 100?
Co-Prime Treasure Vault Code (Section 5.3)
A treasure vault opens only when two numbers entered are co-prime and their product is 630. If both numbers are greater than 10, find all possible valid key pairs.
String Art / Kolam Polygon Formation (Section 5.3)
On a circular ring with 15 evenly spaced pegs numbered 0 to 14, string is wound by jumping 6 pegs each time (0 → 6 → 12 → 3 → 9 → 0). Why does this loop fail to visit all 15 pegs? How many pegs are visited, and what step size WOULD visit all 15?
Factor Tree Branch Invariance for 72 (Section 5.4)
Two students create factor trees for 72: Ananya splits 72 into 8 × 9, while Kabir splits 72 into 6 × 12. Show that both factor trees terminate at the exact same prime building blocks.
Divisibility by Prime Factor Subset (Section 5.4)
Using prime factorisation, determine whether 504 is divisible by 56 and whether 504 is divisible by 48.
Missing Digits for Divisibility by 8 and 5 (Section 5.5)
Find all possible values of the five-digit number 48A5B such that it is divisible by both 5 and 8.
Leap Year Cycle Analysis (Section 5.5)
A child is born on February 29, 2024. In the span from 2024 to 2060, on which exact years will the child celebrate their birthday on the actual date February 29? How many leap day birthdays is that?
The Special 4-Box Number Deduction (Section 5.6)
Consider four numbers: 9, 16, 25, and 43. Provide at least one unique mathematical property for each number that distinguishes it from the other three.
The 3x3 Prime Multiplication Grid (Section 5.6)
A 3x3 grid is filled with prime numbers such that row products are Row 1 = 30, Row 2 = 70, Row 3 = 105, and column products are Col 1 = 42, Col 2 = 50, Col 3 = 105. Find the exact value in each of the 9 cells.
Prime Time – Key Takeaways & Quick Reference
Essential rules, definitions, and theorems to remember for exams.
1. Factors & Multiples
1 is a factor of every number. Every number is a multiple of itself. Factors are finite; multiples are infinite.
2. Prime vs Composite
Primes have exactly 2 factors. 2 is the ONLY even prime. 1 is neither prime nor composite. There are 25 primes ≤ 100.
3. Co-Prime Numbers
Two numbers are co-prime if HCF = 1. Consecutive whole numbers (e.g., 14 & 15) are ALWAYS co-prime!
4. Prime Factorisation
Every composite number has a unique prime factorization. Changing branch order in a factor tree always gives the same primes.
5. Divisibility Tests
÷2 (even unit), ÷4 (last 2 digits), ÷5 (unit 0/5), ÷8 (last 3 digits), ÷10 (unit 0).
6. Thread Art Theorem
On N pins with step gap G, the thread visits ALL N pins if and only if HCF(N, G) = 1 (co-prime).
15 Comprehensive FAQs on Prime Time
Computational Thinking with Prime Numbers & Divisibility
Prime numbers are the fundamental foundation of modern cryptography, RSA encryption algorithms, hash table indexing, and pseudo-random number generators in computer science. Explore our interactive Computational Thinking & AI challenges.