Factors of 49
The factors of 49 are 1, 7, 49. No, 49 is a composite number. Its prime factorization is 7^2.
Factor pairs of 49
Every factor has a partner that multiplies with it to give 49. 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 7 × 7), you have them all.
| Pair | Check |
|---|---|
| 1 and 49 | 1 × 49 = 49 |
| 7 and 7 | 7 × 7 = 49 |
Prime factorization of 49, 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 | 49 ÷ 7 | 7 |
| 2 | 7 ÷ 7 | 1 |
So 49 = 7 × 7, written compactly as 7^2.
Divisibility checks for 49
The quick rules a student uses before dividing, applied to 49:
| Divisible by | Rule | For 49 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 9 | no |
| 3 | digit sum divisible by 3 | digits add to 13 | no |
| 4 | last two digits divisible by 4 | 49 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 9 | no |
| 6 | divisible by both 2 and 3 | odd, digit sum 13 | no |
| 8 | last three digits divisible by 8 | 49 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 13 | no |
| 10 | last digit is 0 | last digit 9 | no |
Frequently Asked Questions
What are the factors of 49?
The factors of 49 are 1, 7, 49.
Is 49 a prime number?
No, 49 is a composite number. Its prime factorization is 7^2.
How many factors does 49 have?
49 has 3 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 7^2 and multiply -- (2+1) = 3.
Is 49 even or odd, and is it a perfect square?
49 is odd (2 is not a factor), and it is a perfect square: 7 × 7 = 49, which is why its factor list has an odd number of entries.
What is the sum of the factors of 49?
1 + 7 + 49 = 57. Leaving out 49 itself, the proper factors add to 8, less than 49, so 49 is a deficient number.
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