Factors of 81
The factors of 81 are 1, 3, 9, 27, 81. No, 81 is a composite number. Its prime factorization is 3^4.
Factor pairs of 81
Every factor has a partner that multiplies with it to give 81. 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 (here at 9 × 9), you have them all.
| Pair | Check |
|---|---|
| 1 and 81 | 1 × 81 = 81 |
| 3 and 27 | 3 × 27 = 81 |
| 9 and 9 | 9 × 9 = 81 |
Prime factorization of 81, 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 | 81 ÷ 3 | 27 |
| 2 | 27 ÷ 3 | 9 |
| 3 | 9 ÷ 3 | 3 |
| 4 | 3 ÷ 3 | 1 |
So 81 = 3 × 3 × 3 × 3, written compactly as 3^4.
Divisibility checks for 81
The quick rules a student uses before dividing, applied to 81:
| Divisible by | Rule | For 81 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 1 | no |
| 3 | digit sum divisible by 3 | digits add to 9 | yes |
| 4 | last two digits divisible by 4 | 81 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 1 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 9 | no |
| 8 | last three digits divisible by 8 | 81 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 9 | yes |
| 10 | last digit is 0 | last digit 1 | no |
Frequently Asked Questions
What are the factors of 81?
The factors of 81 are 1, 3, 9, 27, 81.
Is 81 a prime number?
No, 81 is a composite number. Its prime factorization is 3^4.
How many factors does 81 have?
81 has 5 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 3^4 and multiply -- (4+1) = 5.
Is 81 even or odd, and is it a perfect square?
81 is odd (2 is not a factor), and it is a perfect square: 9 × 9 = 81, which is why its factor list has an odd number of entries.
What is the sum of the factors of 81?
1 + 3 + 9 + 27 + 81 = 121. Leaving out 81 itself, the proper factors add to 40, less than 81, so 81 is a deficient number.
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