How Many Factors Does 360 Have?
360 has 24 factors. You can count them without listing them, by using the prime factorization of 360.
Step 1: Prime Factorization
360 = 2 × 2 × 2 × 3 × 3 × 5, written 2³ × 3² × 5 with exponents.
Step 2: Add 1 to Each Exponent
- 2 has exponent 3, so it gives 3 + 1 = 4 choices
- 3 has exponent 2, so it gives 2 + 1 = 3 choices
- 5 has exponent 1, so it gives 1 + 1 = 2 choices
Step 3: Multiply
(3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24
The Factors of 360
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
That is 24 numbers, which matches the count.
See them paired up on the factors of 360 page.
Is 360 a perfect square?
No. At least one exponent is odd, so 360 is not a perfect square and its factors come in pairs. Count the factors of another number in the Number of Factors Calculator.