Factors of 21
The factors of 21 are 1, 3, 7, 21. No, 21 is a composite number. Its prime factorization is 3 × 7.
Factor pairs of 21
Every factor has a partner that multiplies with it to give 21. 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 21 | 1 × 21 = 21 |
| 3 and 7 | 3 × 7 = 21 |
Prime factorization of 21, 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 | 21 ÷ 3 | 7 |
| 2 | 7 ÷ 7 | 1 |
So 21 = 3 × 7, written compactly as 3 × 7.
Divisibility checks for 21
The quick rules a student uses before dividing, applied to 21:
| Divisible by | Rule | For 21 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 1 | no |
| 3 | digit sum divisible by 3 | digits add to 3 | yes |
| 4 | last two digits divisible by 4 | 21 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 1 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 3 | no |
| 8 | last three digits divisible by 8 | 21 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 3 | no |
| 10 | last digit is 0 | last digit 1 | no |
Frequently Asked Questions
What are the factors of 21?
The factors of 21 are 1, 3, 7, 21.
Is 21 a prime number?
No, 21 is a composite number. Its prime factorization is 3 × 7.
How many factors does 21 have?
21 has 4 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 3 × 7 and multiply -- (1+1) × (1+1) = 4.
Is 21 even or odd?
21 is odd (2 is not a factor).
What is the sum of the factors of 21?
1 + 3 + 7 + 21 = 32. Leaving out 21 itself, the proper factors add to 11, less than 21, so 21 is a deficient number.
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