Factors of 76
The factors of 76 are 1, 2, 4, 19, 38, 76. No, 76 is a composite number. Its prime factorization is 2^2 × 19.
Factor pairs of 76
Every factor has a partner that multiplies with it to give 76. 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 76 | 1 × 76 = 76 |
| 2 and 38 | 2 × 38 = 76 |
| 4 and 19 | 4 × 19 = 76 |
Prime factorization of 76, 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 | 76 ÷ 2 | 38 |
| 2 | 38 ÷ 2 | 19 |
| 3 | 19 ÷ 19 | 1 |
So 76 = 2 × 2 × 19, written compactly as 2^2 × 19.
Divisibility checks for 76
The quick rules a student uses before dividing, applied to 76:
| Divisible by | Rule | For 76 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 6 | yes |
| 3 | digit sum divisible by 3 | digits add to 13 | no |
| 4 | last two digits divisible by 4 | 76 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 6 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 13 | no |
| 8 | last three digits divisible by 8 | 76 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 13 | no |
| 10 | last digit is 0 | last digit 6 | no |
Frequently Asked Questions
What are the factors of 76?
The factors of 76 are 1, 2, 4, 19, 38, 76.
Is 76 a prime number?
No, 76 is a composite number. Its prime factorization is 2^2 × 19.
How many factors does 76 have?
76 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^2 × 19 and multiply -- (2+1) × (1+1) = 6.
Is 76 even or odd?
76 is even (2 is one of its factors).
What is the sum of the factors of 76?
1 + 2 + 4 + 19 + 38 + 76 = 140. Leaving out 76 itself, the proper factors add to 64, less than 76, so 76 is a deficient number.
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