Factors of 98
The factors of 98 are 1, 2, 7, 14, 49, 98. No, 98 is a composite number. Its prime factorization is 2 × 7^2.
Factor pairs of 98
Every factor has a partner that multiplies with it to give 98. 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 98 | 1 × 98 = 98 |
| 2 and 49 | 2 × 49 = 98 |
| 7 and 14 | 7 × 14 = 98 |
Prime factorization of 98, 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 | 98 ÷ 2 | 49 |
| 2 | 49 ÷ 7 | 7 |
| 3 | 7 ÷ 7 | 1 |
So 98 = 2 × 7 × 7, written compactly as 2 × 7^2.
Divisibility checks for 98
The quick rules a student uses before dividing, applied to 98:
| Divisible by | Rule | For 98 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 8 | yes |
| 3 | digit sum divisible by 3 | digits add to 17 | no |
| 4 | last two digits divisible by 4 | 98 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 8 | no |
| 6 | divisible by both 2 and 3 | even, digit sum 17 | no |
| 8 | last three digits divisible by 8 | 98 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 17 | no |
| 10 | last digit is 0 | last digit 8 | no |
Frequently Asked Questions
What are the factors of 98?
The factors of 98 are 1, 2, 7, 14, 49, 98.
Is 98 a prime number?
No, 98 is a composite number. Its prime factorization is 2 × 7^2.
How many factors does 98 have?
98 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2 × 7^2 and multiply -- (1+1) × (2+1) = 6.
Is 98 even or odd?
98 is even (2 is one of its factors).
What is the sum of the factors of 98?
1 + 2 + 7 + 14 + 49 + 98 = 171. Leaving out 98 itself, the proper factors add to 73, less than 98, so 98 is a deficient number.
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