📘 Chapter 5 • Grade 6 Maths

Prime Time

factors ~ multiples ~ primes ~ co-primes ~ divisibility

🔢 ✏️ ➗ ✅ 🧮

📌 Factors & Multiples

Factor of a number → a number that divides it exactly (no remainder).
Example: 4 is a factor of 12, since 12 ÷ 4 = 3.

Multiple of a number → obtained by multiplying it by 1,2,3,...
Multiples of 3 → 3, 6, 9, 12, 15, ...

🔁 Common multiples of 3 & 5 → 15, 30, 45, ... (multiples of both)
🔁 Common factors of 14 & 36 → 1, 2 (numbers that divide both)

Multiples of 3

Multiples of 5

3,6,9,12,18,21,24,27

5,10,20,25,35,40

15,30,45
(common)

🦘 Jump Jackpot idea

Jump-size that lands on a number = factor of that number.

Jump-size landing on two treasures (say 14 & 36) = common factor of both numbers → here, 1 and 2.

🔷 Prime & Composite Numbers

Prime number → exactly 2 factors: 1 and itself.
e.g. 2, 3, 5, 7, 11, 13, 17, 19 ...
Composite number → more than 2 factors.
e.g. 4, 6, 8, 9, 10, 12 ...
1 → neither prime nor composite (only 1 factor) ⚠️
2 → the only even prime number 🌟

🕵️ Sieve of Eratosthenes (finding primes 1–100):

Cross out 1

➜

Circle 2, cross all multiples of 2

➜

Circle next open no. (3), cross its multiples

➜

Repeat with 5, 7 ...

➜

Circled = Primes ✅

⭐ Good-to-know Numbers

Perfect number → sum of all factors = twice the number.
e.g. 6 → factors 1,2,3,6 → sum = 12 = 2 × 6 ✔️
Twin primes → pair of primes differing by 2.
e.g. (3,5), (17,19), (11,13), (29,31)

🤝 Co-prime Numbers

Two numbers are co-prime if their only common factor is 1 (they need not be prime themselves!).

4 and 9 → co-prime ✅ (no common factor except 1)
15 and 39 → not co-prime ❌ (common factor 3)

👉 Any two prime numbers are always co-prime.

👉 If a pair is co-prime, their first common multiple = product of the two numbers.

🌳 Prime Factorisation

Writing a number as a product of only prime numbers.

4 × 14

2×2 × 2×7

2×2×2×7

✏️ Every number > 1 has exactly one prime factorisation (order doesn't matter).
✏️ Number 1 → no prime factorisation. A prime number's own factorisation is itself.

🎯 Uses of Prime Factorisation:

Check co-prime: No common prime factor → co-prime.
56 = 2×2×2×7, 63 = 3×3×7 → share 7 → NOT co-prime
Check divisibility: If 2nd number's prime factors are fully contained in 1st → divisible.
168 = 2×2×2×3×7, 12 = 2×2×3 → 12's factors present in 168 → 168 ÷ 12 ✔️

➗ Divisibility Rules

Divisible by	Rule	Example
2	last digit is 0,2,4,6,8	682 ✔️
5	last digit is 0 or 5	8560 ✔️
10	last digit is 0	8560 ✔️
4	last 2 digits divisible by 4	8536 → 36÷4 ✔️
8	last 3 digits divisible by 8	8536 → 536÷8 ✔️

🔮 Rules for 3, 6, 7, 9 → coming in later classes!

✅ Quick Revision Checklist

I can find factors & multiples of a number

I can find common factors & common multiples

I know the difference between prime & composite numbers

I can use the Sieve of Eratosthenes

I understand co-prime numbers & how to check them

I can find the prime factorisation of a number

I can use prime factorisation to check co-primality & divisibility

I know divisibility rules for 2, 4, 5, 8, 10

I know what perfect numbers & twin primes are