Class 6 Mathematics · 9 min read · Published 10 October 2026

Factors and Multiples for Class 6: Difference, Prime Numbers and Solved Examples

By Dishantra Editorial · Reviewed 10 October 2026

Factors and multiples are closely connected. That is also why they are easy to mix up. Take 12: its factors include 1, 2, 3, 4, 6 and 12, while its positive multiples include 12, 24, 36, 48, 60…

The two lists are different because they answer opposite questions.

1. What is a factor?

A factor divides a number exactly. For 12:

“Divides exactly” means the division leaves no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4, while 5 is not a factor of 12 because the division does not produce a whole-number quotient.

1 × 12 = 12 · 2 × 6 = 12 · 3 × 4 = 12

So the positive factors of 12 are 1, 2, 3, 4, 6, 12.

A positive whole number has a finite number of positive factors.

2. What is a multiple?

Positive multiples of 6 are obtained by multiplying 6 by positive whole numbers:

Multiples answer a forward-looking question: what numbers appear when we keep counting in equal groups of the original number? That is why the list keeps growing, unlike the finite list of positive factors.

6, 12, 18, 24, 30, …

The list continues without end. (If your class includes 0 as a whole-number multiplier, 0 is also a multiple; here we list positive multiples because that is the form used in the examples below.)

3. Factor vs multiple

A useful clue: positive factors of a positive whole number do not exceed that number; positive multiples continue beyond it.

4. What is a prime number?

A prime number has exactly two positive factors: 1 and itself. Examples include 2, 3, 5, 7, 11 and 13. The number 7 has only the positive factors 1 and 7, so it is prime.

The number 2 is special because it is the only even prime number. Every other even positive integer greater than 2 is divisible by 2 as well as by 1 and itself, so it has more than two positive factors.

5. What is a composite number?

A composite number has more than two positive factors. For example, 12 has 1, 2, 3, 4, 6 and 12, so it is composite.

1 is neither prime nor composite because it has only one positive factor.

6. Prime factorisation

Prime factorisation expresses a composite number as a product of prime numbers. For 36:

Different first splits can still lead to the same prime factors. For 36, you might begin with 4 × 9 instead of 6 × 6. Continuing until every factor is prime still gives 2 × 2 × 3 × 3.

7. Common factors

Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

“Common” means appearing in both lists. Listing factors systematically helps avoid missing one. If a question later asks for the greatest common factor, choose the largest number in the common list.

The common factors are 1, 2, 3 and 6. The greatest of these is 6.

8. Common multiples

Positive multiples of 4: 4, 8, 12, 16, 20, 24…
Positive multiples of 6: 6, 12, 18, 24…

Again, “common” means appearing in both lists. The first positive number that appears in both lists is the smallest positive common multiple. Listing is a useful introductory method because the relationship remains visible.

The smallest positive common multiple is 12.

This guide introduces common factors and common multiples but deliberately does not expand into a full HCF/LCM chapter; that would be a separate search job if demand justifies it.

9. How factors and multiples connect

10. Common mistakes

• Calling 24 a factor of 6. It is a multiple of 6, not a factor.
• Saying 1 is prime. Prime numbers have exactly two positive factors; 1 has one.
• Stopping a factor tree at 36 = 4 × 9 even though 4 and 9 are not prime.
• Thinking positive multiples eventually stop. You can always multiply by another positive whole number.

Quick check

The key distinction

Ask: Does this number divide the original number exactly? If yes, it may be a factor. Ask: Did I obtain this number by multiplying the original by a whole-number multiplier? If yes, it is a multiple.

Once that distinction is secure, prime numbers, common factors, common multiples and prime factorisation become much easier to organise.