Factors Calculator: All Factors and Factor Pairs

How to use the factors calculator

Enter a whole number.
Read the sorted list of factors.
Open the steps for the factor pairs.
Check the number type notes.

Facts

d is a factor of n if n ÷ d is a whole number
Factors come in pairs (d, n/d)
Number of factors = Π (exponent + 1) over the prime factorization

A perfect number equals the sum of its factors below itself, like 6 and 28.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

Answer9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36

36 is composite
Sum of factors 91
An abundant number

Step-by-step working 3 steps

1
Test divisors up to the square root
Only divisors up to √36 ≈ 6 need testing; each one found has a partner.

Factor pairs

1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36

3
All factors in order
```
1, 2, 3, 4, 6, 9, 12, 18, 36
```

28 (perfect)

Answer6 factors: 1, 2, 4, 7, 14, 28

28 is composite
Sum of factors 56
A perfect number

Step-by-step working 3 steps

1
Test divisors up to the square root
Only divisors up to √28 ≈ 5.2915 need testing; each one found has a partner.
2
Factor pairs
```
1 × 28 = 28
2 × 14 = 28
4 × 7 = 28
```
3
All factors in order
```
1, 2, 4, 7, 14, 28
```

97 (prime)

Answer2 factors: 1, 97

97 is prime
Sum of factors 98
A deficient number

Step-by-step working 3 steps

1
Test divisors up to the square root
Only divisors up to √97 ≈ 9.8489 need testing; each one found has a partner.
2
Factor pairs
```
1 × 97 = 97
```
3
All factors in order
```
1, 97
```

360

Answer24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

360 is composite
Sum of factors 1,170
An abundant number

Step-by-step working 3 steps

1
Test divisors up to the square root
Only divisors up to √360 ≈ 18.9737 need testing; each one found has a partner.

Factor pairs

1 × 360 = 360
2 × 180 = 360
3 × 120 = 360
4 × 90 = 360
5 × 72 = 360
6 × 60 = 360
8 × 45 = 360
9 × 40 = 360
10 × 36 = 360
12 × 30 = 360
15 × 24 = 360
18 × 20 = 360

All factors in order

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Common mistakes to avoid

Forgetting 1 and the number itself

Both are always factors.

Testing too far

You only need to test up to √n; each factor found has a partner.

Confusing factors and multiples

Factors divide n; multiples are n times something.

Frequently asked questions

Which numbers have an odd number of factors?

Perfect squares, because one factor pairs with itself.