# What are the Factors of 98?

Factors of 98 are any integer that can be multiplied by another integer to make exactly 98. In other words, finding the factors of 98 is like breaking down the number 98 into all the smaller pieces that can be used in a multiplication problem to equal 98.

## Factors of 98

Methods

### What are the Factors of 98?

The following are the different types of factors of 98:

• Factors of 98: 1, 2, 7, 14, 49, 98

• Sum of Factors of 98: 171

• Negative Factors of 98: -1, -2, -7, -14, -49, -98

• Prime Factors of 98: 2, 7

• Prime Factorization of 98: 2^1 × 7^2

There are two ways to find the factors of 98: using factor pairs, and using prime factorization.

### The Factor Pairs of 98

Factor pairs of 98 are any two numbers that, when multiplied together, equal 98. The question to ask is “what two numbers multiplied together equal 98?” Every factor can be paired with another factor, and multiplying the two will result in 98.

To find the factor pairs of 98, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 98. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.

Step 2:

Divide 98 by the smallest prime factor, in this case, 2:

98 ÷ 2 = 49

2 and 49 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 49 as the new focus. Find the smallest prime factor that isn’t 1, and divide 49 by that number. In this case, 7 is the new smallest prime factor:

49 ÷ 7 = 7

Remember that this new factor pair is only for the factors of 49, not 98. So, to finish the factor pair for 98, you’d multiply 2 and 7 before pairing with 7:

2 x 7 = 14

Step 4:

Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.

Here are all the factor pairs for 98:

(1, 98), (2, 49), (7, 14)

So, to list all the factors of 98: 1, 2, 7, 14, 49, 98

The negative factors of 98 would be: -1, -2, -7, -14, -49, -98

### Prime Factorization of 98

To find the Prime factorization of 98, we break down all the factors of 98 until we are left with only prime factors. We then express n as a product of multiplying the prime factors together.

The process of finding the prime factorization of 98 only has a few differences from the above method of finding the factors of 98. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.

Here are the steps for finding the prime factorization of 98:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 98. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.

Step 2:

Divide 98 by the smallest prime factor, in this case, 2

98 ÷ 2 = 49

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 49 as the new focus. Find the smallest prime factor that isn’t 1, and divide 49 by that number. The smallest prime factor you pick for 49 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.

So, the unique prime factors of 98 are: 2, 7

### Find the Factors of Other Numbers

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 65 - The factors of 65 are 1, 5, 13, 65

Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63

Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50

Factors of 115 - The factors of 115 are 1, 5, 23, 115

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