Factors of 61
The factors of 61 are 1, 61. Yes, 61 is a prime number. Its only factors are 1 and 61.
Factor pairs of 61
Every factor has a partner that multiplies with it to give 61. 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 61 | 1 × 61 = 61 |
Prime factorization of 61, step by step
61 is prime, so the ladder is one rung: nothing smaller than 61 divides it except 1. To confirm, you only need to test primes up to √61 ≈ 7: 61 ÷ 2 leaves 1; 61 ÷ 3 leaves 1; 61 ÷ 5 leaves 1; 61 ÷ 7 leaves 5.
Divisibility checks for 61
The quick rules a student uses before dividing, applied to 61:
| Divisible by | Rule | For 61 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 1 | no |
| 3 | digit sum divisible by 3 | digits add to 7 | no |
| 4 | last two digits divisible by 4 | 61 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 1 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 7 | no |
| 8 | last three digits divisible by 8 | 61 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 7 | no |
| 10 | last digit is 0 | last digit 1 | no |
Frequently Asked Questions
What are the factors of 61?
The factors of 61 are 1, 61.
Is 61 a prime number?
Yes, 61 is a prime number. Its only factors are 1 and 61.
How many factors does 61 have?
61 has 2 factors.
Is 61 even or odd?
61 is odd (2 is not a factor).
What is the sum of the factors of 61?
1 + 61 = 62. Leaving out 61 itself, the proper factors add to 1, less than 61, so 61 is a deficient number.
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