Factor Calculator
All factor pairs of a number
About This Calculator
A factor of a number n is any integer that divides n with no remainder. Finding all factors is useful in simplifying fractions, finding GCD, solving equations, and understanding divisibility. The number of factors can be determined from the prime factorization of n.
Formula
f is a factor of n if n mod f = 0
If n = p^a × q^b × ..., then factor count = (a+1)(b+1)...
Example Calculation
Find all factors of 36.
- Test 1 through sqrt(36)=6: 1, 2, 3, 4, 6 all divide 36
- Paired factors: 36/1=36, 36/2=18, 36/3=12, 36/4=9, 36/6=6
- All factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
36 has 9 factors
Factors of Common Numbers
| Number | Factor Count | All Factors |
|---|---|---|
| 12 | 6 | 1, 2, 3, 4, 6, 12 |
| 24 | 8 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 36 | 9 | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| 48 | 10 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |
| 60 | 12 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 |
| 100 | 9 | 1, 2, 4, 5, 10, 20, 25, 50, 100 |
Frequently Asked Questions
What is the difference between a factor and a multiple?
A factor divides into a number evenly (factors of 12 are 1,2,3,4,6,12). A multiple is what you get by multiplying (multiples of 12 are 12,24,36,...).
How do I know when I have found all the factors?
Only test divisors up to the square root of n. Each divisor below sqrt(n) pairs with one above it. When you reach sqrt(n), you have them all.
What is a perfect number?
A perfect number equals the sum of its proper factors (all factors except itself). 6 = 1+2+3 and 28 = 1+2+4+7+14 are the two smallest perfect numbers.