Factors of 65
The factors of 65 are 1, 5, 13, 65. No, 65 is a composite number. Its prime factorization is 5 × 13.
Factor pairs of 65
Every factor has a partner that multiplies with it to give 65. 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, you have them all.
| Pair | Check |
|---|---|
| 1 and 65 | 1 × 65 = 65 |
| 5 and 13 | 5 × 13 = 65 |
Prime factorization of 65, 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 | 65 ÷ 5 | 13 |
| 2 | 13 ÷ 13 | 1 |
So 65 = 5 × 13, written compactly as 5 × 13.
Divisibility checks for 65
The quick rules a student uses before dividing, applied to 65:
| Divisible by | Rule | For 65 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 5 | no |
| 3 | digit sum divisible by 3 | digits add to 11 | no |
| 4 | last two digits divisible by 4 | 65 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 5 | yes |
| 6 | divisible by both 2 and 3 | odd, digit sum 11 | no |
| 8 | last three digits divisible by 8 | 65 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 11 | no |
| 10 | last digit is 0 | last digit 5 | no |
Frequently Asked Questions
What are the factors of 65?
The factors of 65 are 1, 5, 13, 65.
Is 65 a prime number?
No, 65 is a composite number. Its prime factorization is 5 × 13.
How many factors does 65 have?
65 has 4 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 5 × 13 and multiply -- (1+1) × (1+1) = 4.
Is 65 even or odd?
65 is odd (2 is not a factor).
What is the sum of the factors of 65?
1 + 5 + 13 + 65 = 84. Leaving out 65 itself, the proper factors add to 19, less than 65, so 65 is a deficient number.
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