Factors of 48
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. No, 48 is a composite number. Its prime factorization is 2^4 × 3.
Factor pairs of 48
Every factor has a partner that multiplies with it to give 48. 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 48 | 1 × 48 = 48 |
| 2 and 24 | 2 × 24 = 48 |
| 3 and 16 | 3 × 16 = 48 |
| 4 and 12 | 4 × 12 = 48 |
| 6 and 8 | 6 × 8 = 48 |
Prime factorization of 48, 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 | 48 ÷ 2 | 24 |
| 2 | 24 ÷ 2 | 12 |
| 3 | 12 ÷ 2 | 6 |
| 4 | 6 ÷ 2 | 3 |
| 5 | 3 ÷ 3 | 1 |
So 48 = 2 × 2 × 2 × 2 × 3, written compactly as 2^4 × 3.
Divisibility checks for 48
The quick rules a student uses before dividing, applied to 48:
| Divisible by | Rule | For 48 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 8 | yes |
| 3 | digit sum divisible by 3 | digits add to 12 | yes |
| 4 | last two digits divisible by 4 | 48 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 8 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 12 | yes |
| 8 | last three digits divisible by 8 | 48 ÷ 8 | yes |
| 9 | digit sum divisible by 9 | digits add to 12 | no |
| 10 | last digit is 0 | last digit 8 | no |
Frequently Asked Questions
What are the factors of 48?
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Is 48 a prime number?
No, 48 is a composite number. Its prime factorization is 2^4 × 3.
How many factors does 48 have?
48 has 10 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^4 × 3 and multiply -- (4+1) × (1+1) = 10.
Is 48 even or odd?
48 is even (2 is one of its factors).
What is the sum of the factors of 48?
1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124. Leaving out 48 itself, the proper factors add to 76, more than 48, so 48 is an abundant number.
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