Factors of 67
The factors of 67 are 1, 67. Yes, 67 is a prime number. Its only factors are 1 and 67.
Factor pairs of 67
Every factor has a partner that multiplies with it to give 67. 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 67 | 1 × 67 = 67 |
Prime factorization of 67, step by step
67 is prime, so the ladder is one rung: nothing smaller than 67 divides it except 1. To confirm, you only need to test primes up to √67 ≈ 8: 67 ÷ 2 leaves 1; 67 ÷ 3 leaves 1; 67 ÷ 5 leaves 2; 67 ÷ 7 leaves 4.
Divisibility checks for 67
The quick rules a student uses before dividing, applied to 67:
| Divisible by | Rule | For 67 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 7 | no |
| 3 | digit sum divisible by 3 | digits add to 13 | no |
| 4 | last two digits divisible by 4 | 67 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 7 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 13 | no |
| 8 | last three digits divisible by 8 | 67 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 13 | no |
| 10 | last digit is 0 | last digit 7 | no |
Frequently Asked Questions
What are the factors of 67?
The factors of 67 are 1, 67.
Is 67 a prime number?
Yes, 67 is a prime number. Its only factors are 1 and 67.
How many factors does 67 have?
67 has 2 factors.
Is 67 even or odd?
67 is odd (2 is not a factor).
What is the sum of the factors of 67?
1 + 67 = 68. Leaving out 67 itself, the proper factors add to 1, less than 67, so 67 is a deficient number.
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