Factors & Multiples — Class 4 IMO

Factors, Prime & Composite Numbers

A factor of a number divides it exactly with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. Every number has 1 and itself as factors.

A prime number has exactly two factors — 1 and itself (2, 3, 5, 7, 11…). A composite number has more than two factors (4, 6, 8, 9…). The number 1 is neither prime nor composite.

Example 1: List all the factors of 18.

1, 2, 3, 6, 9 and 18.

Example 2: Is 7 a prime or composite number?

Prime — its only factors are 1 and 7.

Quick recap

A factor divides a number exactly.
Prime = exactly two factors; composite = more than two.
1 is neither prime nor composite.

✓ Quick check

Which of these is a prime number?

11 has only the factors 1 and 11, so it is prime.

How many factors does 6 have?

The factors of 6 are 1, 2, 3 and 6 — that is 4 factors.

Multiples & Divisibility Rules

A multiple is what you get by multiplying a number by 1, 2, 3, and so on. The multiples of 4 are 4, 8, 12, 16, 20…

Divisibility rules help us check quickly: a number is divisible by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, by 10 if it ends in 0, and by 3 if the sum of its digits is divisible by 3.

Example 1: Write the first three multiples of 6.

6, 12 and 18.

Example 2: Is 123 divisible by 3?

Digit sum 1 + 2 + 3 = 6, which is divisible by 3, so yes.

Quick recap

Multiples come from multiplying by 1, 2, 3, …
Divisible by 2 (even), 5 (ends 0/5), 10 (ends 0), 3 (digit sum ÷ 3).

✓ Quick check

Which number is a multiple of 7?

7 × 5 = 35, so 35 is a multiple of 7.

Which number is divisible by 10?

250 ends in 0, so it is divisible by 10.

HCF & LCM by Listing

The HCF (Highest Common Factor) of two numbers is the largest factor they share. List the factors of each and pick the biggest common one. The factors of 12 are 1, 2, 3, 4, 6, 12 and of 18 are 1, 2, 3, 6, 9, 18 — the HCF is 6.

The LCM (Lowest Common Multiple) is the smallest multiple they share. The first common multiple of 4 and 6 is 12, so the LCM is 12.

Example 1: Find the HCF of 8 and 12.

Common factors are 1, 2, 4; the highest is 4.

Example 2: Find the LCM of 3 and 4.

The smallest common multiple of 3 and 4 is 12.

Quick recap

HCF = the largest common factor.
LCM = the smallest common multiple.

✓ Quick check

What is the HCF of 6 and 9?

Common factors of 6 and 9 are 1 and 3; the highest is 3.

What is the LCM of 2 and 5?

The smallest common multiple of 2 and 5 is 10.