Factor Calculator · Practical guide
How Many Factors Does a Number Have?
Add 1 to each exponent in the prime factorization and multiply: 360 = 2^3 x 3^2 x 5^1 has 4 x 3 x 2 = 24 factors.
At a glance
The Factor-Count Formula
You do not need to list every factor to count them. Write the number as a product of prime powers, add 1 to each exponent, and multiply. Take 360 = 2^3 x 3^2 x 5^1: the count is (3+1) x (2+1) x (1+1) = 4 x 3 x 2 = 24 factors. This works because each factor of 360 is built by choosing a power of 2 from 0 to 3, a power of 3 from 0 to 2, and a power of 5 from 0 to 1.
Interactive tool
Factor Calculator
Enter your own values, then compare the result with the examples below.
Result
Factor Counts for Common Numbers
| Number | Prime Factorization | Calculation | Factor Count |
|---|---|---|---|
| 12 | 2^2 x 3 | 3 x 2 | 6 |
| 36 | 2^2 x 3^2 | 3 x 3 | 9 |
| 60 | 2^2 x 3 x 5 | 3 x 2 x 2 | 12 |
| 360 | 2^3 x 3^2 x 5 | 4 x 3 x 2 | 24 |
| 720 | 2^4 x 3^2 x 5 | 5 x 3 x 2 | 30 |
Special Cases Worth Knowing
- Prime numbers have exactly 2 factors — the exponent is 1, so (1+1) = 2.
- Perfect squares like 36 always have an odd count, because all exponents are even, so every (exponent+1) is odd.
- Prime powers like 32 = 2^5 have exponent+1 factors — 6 in this case: 1, 2, 4, 8, 16, 32.
- Highly composite numbers like 360 pack many factors into a small size, which is why they show up in packaging, timekeeping, and carpentry.
Verify Instantly
The calculator above lists every factor of any positive integer up to one trillion and reports the exact count alongside the sum — a quick way to confirm your exponent arithmetic.
Frequently Asked Questions
Why do perfect squares have an odd number of factors?
Factors normally pair up (1 with n, 2 with n/2, and so on). In a perfect square, the square root pairs with itself and is counted once, leaving an odd total.
What number under 100 has the most factors?
Several tie at 12 factors: 60, 72, 84, 90, and 96. No number under 100 has more than 12.
Does 1 have any factors?
Just one: itself. The formula gives (no primes), and 1 is special — it is neither prime nor composite.
Can two different numbers have the same factor count?
Yes, constantly. 6 and 8 both have 4 factors. The count depends only on the pattern of exponents in the prime factorization, not on which primes are involved.