Factors of 78
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. No, 78 is a composite number. Its prime factorization is 2 × 3 × 13.
Factor pairs of 78
Every factor has a partner that multiplies with it to give 78. 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 78 | 1 × 78 = 78 |
| 2 and 39 | 2 × 39 = 78 |
| 3 and 26 | 3 × 26 = 78 |
| 6 and 13 | 6 × 13 = 78 |
Prime factorization of 78, 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 | 78 ÷ 2 | 39 |
| 2 | 39 ÷ 3 | 13 |
| 3 | 13 ÷ 13 | 1 |
So 78 = 2 × 3 × 13, written compactly as 2 × 3 × 13.
Divisibility checks for 78
The quick rules a student uses before dividing, applied to 78:
| Divisible by | Rule | For 78 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 8 | yes |
| 3 | digit sum divisible by 3 | digits add to 15 | yes |
| 4 | last two digits divisible by 4 | 78 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 8 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 15 | yes |
| 8 | last three digits divisible by 8 | 78 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 15 | no |
| 10 | last digit is 0 | last digit 8 | no |
Frequently Asked Questions
What are the factors of 78?
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.
Is 78 a prime number?
No, 78 is a composite number. Its prime factorization is 2 × 3 × 13.
How many factors does 78 have?
78 has 8 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2 × 3 × 13 and multiply -- (1+1) × (1+1) × (1+1) = 8.
Is 78 even or odd?
78 is even (2 is one of its factors).
What is the sum of the factors of 78?
1 + 2 + 3 + 6 + 13 + 26 + 39 + 78 = 168. Leaving out 78 itself, the proper factors add to 90, more than 78, so 78 is an abundant number.
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