Factors of 84
Every whole number that divides 84 exactly, the factor pairs, and how to find them yourself.
The answer
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.
Factor pairs of 84
| Pair | Makes |
|---|---|
| 1 × 84 | 84 |
| 2 × 42 | 84 |
| 3 × 28 | 84 |
| 4 × 21 | 84 |
| 6 × 14 | 84 |
| 7 × 12 | 84 |
Prime factors of 84
- Prime factorisation
- 84 = 2 × 2 × 3 × 7 (2² × 3 × 7)
- Reading index form
- A small raised number tells you how many times to use that factor. For example, 2³ means 2 × 2 × 2.
- Is 84 prime?
- No. It has 12 factors, not just 1 and 84.
- Is 84 a square number?
- No. 9 × 9 = 81 and 10 × 10 = 100, so 84 falls between two square numbers.
How to find the factors of 84
84 is even, so 2 is sure to be a factor. Its digits add up to 12, a multiple of 3, so 3 is a factor. Work up from 1 to 9, and write down both numbers in every pair you find.
- 84 ÷ 1 = 84, so 1 × 84 is a pair.
- 84 ÷ 2 = 42, so 2 × 42 is a pair.
- 84 ÷ 3 = 28, so 3 × 28 is a pair.
- 84 ÷ 4 = 21, so 4 × 21 is a pair.
- 5 does not go into 84 exactly.
- 84 ÷ 6 = 14, so 6 × 14 is a pair.
- 84 ÷ 7 = 12, so 7 × 12 is a pair.
- 8 does not go into 84 exactly.
- 9 does not go into 84 exactly.
Stop at 10: 10 × 10 = 100, which is more than 84. The next pair you would find is 12 × 7, which is 7 × 12 turned round, so you already have every pair.
84 in the times tables
6 × 14 = 84 and 7 × 12 = 84. Practise the 7 times table, 12 times table and 14 times table.
More numbers
Check whether 84 is prime.
Questions parents ask
What is the largest factor of 84, apart from 84 itself?
42. Divide 84 by its smallest factor above 1, which is 2: 84 ÷ 2 = 42.
What do the factors of 84 add up to?
224. Leaving out 84 itself, they add up to 140, which is more than 84, so 84 is called an abundant number.
Which number after 84 has the same number of factors?
90. Like 84, it has exactly 12 factors.
Continue your number practice
Explore the diagnostic for another set of practice questions.