Factors of 64
The factors of 64 are 1, 2, 4, 8, 16, 32, 64. No, 64 is a composite number. Its prime factorization is 2^6.
Factor pairs of 64
Every factor has a partner that multiplies with it to give 64. Listing pairs from the outside in is the fastest way to find all the factors: once the two numbers in a pair meet in the middle (here at 8 × 8), you have them all.
| Pair | Check |
|---|---|
| 1 and 64 | 1 × 64 = 64 |
| 2 and 32 | 2 × 32 = 64 |
| 4 and 16 | 4 × 16 = 64 |
| 8 and 8 | 8 × 8 = 64 |
Prime factorization of 64, step by step
Divide by the smallest prime that goes in evenly, then repeat on the result until you reach 1. The divisors you used are the prime factors.
| Step | Divide | Result |
|---|---|---|
| 1 | 64 ÷ 2 | 32 |
| 2 | 32 ÷ 2 | 16 |
| 3 | 16 ÷ 2 | 8 |
| 4 | 8 ÷ 2 | 4 |
| 5 | 4 ÷ 2 | 2 |
| 6 | 2 ÷ 2 | 1 |
So 64 = 2 × 2 × 2 × 2 × 2 × 2, written compactly as 2^6.
Divisibility checks for 64
The quick rules a student uses before dividing, applied to 64:
| Divisible by | Rule | For 64 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 4 | yes |
| 3 | digit sum divisible by 3 | digits add to 10 | no |
| 4 | last two digits divisible by 4 | 64 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 4 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 10 | no |
| 8 | last three digits divisible by 8 | 64 ÷ 8 | yes |
| 9 | digit sum divisible by 9 | digits add to 10 | no |
| 10 | last digit is 0 | last digit 4 | no |
Frequently Asked Questions
What are the factors of 64?
The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Is 64 a prime number?
No, 64 is a composite number. Its prime factorization is 2^6.
How many factors does 64 have?
64 has 7 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^6 and multiply -- (6+1) = 7.
Is 64 even or odd, and is it a perfect square?
64 is even (2 is one of its factors), and it is a perfect square: 8 × 8 = 64, which is why its factor list has an odd number of entries.
What is the sum of the factors of 64?
1 + 2 + 4 + 8 + 16 + 32 + 64 = 127. Leaving out 64 itself, the proper factors add to 63, less than 64, so 64 is a deficient number.
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