Factors of 68
The factors of 68 are 1, 2, 4, 17, 34, 68. No, 68 is a composite number. Its prime factorization is 2^2 × 17.
Factor pairs of 68
Every factor has a partner that multiplies with it to give 68. 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 68 | 1 × 68 = 68 |
| 2 and 34 | 2 × 34 = 68 |
| 4 and 17 | 4 × 17 = 68 |
Prime factorization of 68, 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 | 68 ÷ 2 | 34 |
| 2 | 34 ÷ 2 | 17 |
| 3 | 17 ÷ 17 | 1 |
So 68 = 2 × 2 × 17, written compactly as 2^2 × 17.
Divisibility checks for 68
The quick rules a student uses before dividing, applied to 68:
| Divisible by | Rule | For 68 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 8 | yes |
| 3 | digit sum divisible by 3 | digits add to 14 | no |
| 4 | last two digits divisible by 4 | 68 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 8 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 14 | no |
| 8 | last three digits divisible by 8 | 68 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 14 | no |
| 10 | last digit is 0 | last digit 8 | no |
Frequently Asked Questions
What are the factors of 68?
The factors of 68 are 1, 2, 4, 17, 34, 68.
Is 68 a prime number?
No, 68 is a composite number. Its prime factorization is 2^2 × 17.
How many factors does 68 have?
68 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^2 × 17 and multiply -- (2+1) × (1+1) = 6.
Is 68 even or odd?
68 is even (2 is one of its factors).
What is the sum of the factors of 68?
1 + 2 + 4 + 17 + 34 + 68 = 126. Leaving out 68 itself, the proper factors add to 58, less than 68, so 68 is a deficient number.
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