Factors of 35
The factors of 35 are 1, 5, 7, 35. No, 35 is a composite number. Its prime factorization is 5 × 7.
Factor pairs of 35
Every factor has a partner that multiplies with it to give 35. 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 35 | 1 × 35 = 35 |
| 5 and 7 | 5 × 7 = 35 |
Prime factorization of 35, 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 | 35 ÷ 5 | 7 |
| 2 | 7 ÷ 7 | 1 |
So 35 = 5 × 7, written compactly as 5 × 7.
Divisibility checks for 35
The quick rules a student uses before dividing, applied to 35:
| Divisible by | Rule | For 35 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 5 | no |
| 3 | digit sum divisible by 3 | digits add to 8 | no |
| 4 | last two digits divisible by 4 | 35 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 5 | yes |
| 6 | divisible by both 2 and 3 | odd, digit sum 8 | no |
| 8 | last three digits divisible by 8 | 35 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 8 | no |
| 10 | last digit is 0 | last digit 5 | no |
Frequently Asked Questions
What are the factors of 35?
The factors of 35 are 1, 5, 7, 35.
Is 35 a prime number?
No, 35 is a composite number. Its prime factorization is 5 × 7.
How many factors does 35 have?
35 has 4 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 5 × 7 and multiply -- (1+1) × (1+1) = 4.
Is 35 even or odd?
35 is odd (2 is not a factor).
What is the sum of the factors of 35?
1 + 5 + 7 + 35 = 48. Leaving out 35 itself, the proper factors add to 13, less than 35, so 35 is a deficient number.
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