Factors of 66
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. No, 66 is a composite number. Its prime factorization is 2 × 3 × 11.
Factor pairs of 66
Every factor has a partner that multiplies with it to give 66. 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 66 | 1 × 66 = 66 |
| 2 and 33 | 2 × 33 = 66 |
| 3 and 22 | 3 × 22 = 66 |
| 6 and 11 | 6 × 11 = 66 |
Prime factorization of 66, 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 | 66 ÷ 2 | 33 |
| 2 | 33 ÷ 3 | 11 |
| 3 | 11 ÷ 11 | 1 |
So 66 = 2 × 3 × 11, written compactly as 2 × 3 × 11.
Divisibility checks for 66
The quick rules a student uses before dividing, applied to 66:
| Divisible by | Rule | For 66 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 6 | yes |
| 3 | digit sum divisible by 3 | digits add to 12 | yes |
| 4 | last two digits divisible by 4 | 66 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 6 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 12 | yes |
| 8 | last three digits divisible by 8 | 66 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 12 | no |
| 10 | last digit is 0 | last digit 6 | no |
Frequently Asked Questions
What are the factors of 66?
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Is 66 a prime number?
No, 66 is a composite number. Its prime factorization is 2 × 3 × 11.
How many factors does 66 have?
66 has 8 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2 × 3 × 11 and multiply -- (1+1) × (1+1) × (1+1) = 8.
Is 66 even or odd?
66 is even (2 is one of its factors).
What is the sum of the factors of 66?
1 + 2 + 3 + 6 + 11 + 22 + 33 + 66 = 144. Leaving out 66 itself, the proper factors add to 78, more than 66, so 66 is an abundant number.
More Number Theory
- Factor Calculator (look up any number)
- GCF Calculator
- LCM Calculator
- LCD Calculator