Factors of 75
The factors of 75 are 1, 3, 5, 15, 25, 75. No, 75 is a composite number. Its prime factorization is 3 × 5^2.
Factor pairs of 75
Every factor has a partner that multiplies with it to give 75. 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 75 | 1 × 75 = 75 |
| 3 and 25 | 3 × 25 = 75 |
| 5 and 15 | 5 × 15 = 75 |
Prime factorization of 75, 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 | 75 ÷ 3 | 25 |
| 2 | 25 ÷ 5 | 5 |
| 3 | 5 ÷ 5 | 1 |
So 75 = 3 × 5 × 5, written compactly as 3 × 5^2.
Divisibility checks for 75
The quick rules a student uses before dividing, applied to 75:
| Divisible by | Rule | For 75 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 5 | no |
| 3 | digit sum divisible by 3 | digits add to 12 | yes |
| 4 | last two digits divisible by 4 | 75 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 5 | yes |
| 6 | divisible by both 2 and 3 | odd, digit sum 12 | no |
| 8 | last three digits divisible by 8 | 75 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 12 | no |
| 10 | last digit is 0 | last digit 5 | no |
Frequently Asked Questions
What are the factors of 75?
The factors of 75 are 1, 3, 5, 15, 25, 75.
Is 75 a prime number?
No, 75 is a composite number. Its prime factorization is 3 × 5^2.
How many factors does 75 have?
75 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 3 × 5^2 and multiply -- (1+1) × (2+1) = 6.
Is 75 even or odd?
75 is odd (2 is not a factor).
What is the sum of the factors of 75?
1 + 3 + 5 + 15 + 25 + 75 = 124. Leaving out 75 itself, the proper factors add to 49, less than 75, so 75 is a deficient number.
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