What are the Factors of 118?

The following are the different types of factors of 118:

• Factors of 118: 1, 2, 59, 118

• Sum of Factors of 118: 180

• Negative Factors of 118: -1, -2, -59, -118

• Prime Factors of 118: 2, 59

• Prime Factorization of 118: 2^1 × 59^1

There are two ways to find the factors of 118: using factor pairs, and using prime factorization.

Factor pairs of 118 are any two numbers that, when multiplied together, equal 118. The question to ask is “what two numbers multiplied together equal 118?” Every factor can be paired with another factor, and multiplying the two will result in 118.

To find the factor pairs of 118, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 118. 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 118 by the smallest prime factor, in this case, 2:

118 ÷ 2 = 59

2 and 59 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 59 as the new focus. Find the smallest prime factor that isn’t 1, and divide 59 by that number. In this case, 59 is the new smallest prime factor:

59 ÷ 59 = 1

Remember that this new factor pair is only for the factors of 59, not 118. So, to finish the factor pair for 118, you’d multiply 2 and 59 before pairing with 1:

2 x 59 = 118

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 118:

(1, 118), (2, 59)

So, to list all the factors of 118: 1, 2, 59, 118

The negative factors of 118 would be: -1, -2, -59, -118

To find the Prime factorization of 118, we break down all the factors of 118 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 118 only has a few differences from the above method of finding the factors of 118. 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 118:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 118. 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 118 by the smallest prime factor, in this case, 2

118 ÷ 2 = 59

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 59 as the new focus. Find the smallest prime factor that isn’t 1, and divide 59 by that number. The smallest prime factor you pick for 59 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 118 are: 2, 59

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

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

Factors of 67 - The factors of 67 are 1, 67

Factors of 126 - The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

Factors of 117 - The factors of 117 are 1, 3, 9, 13, 39, 117