What are the Factors of 57?

Factors of 57 are any integer that can be multiplied by another integer to make exactly 57. In other words, finding the factors of 57 is like breaking down the number 57 into all the smaller pieces that can be used in a multiplication problem to equal 57.

Factors of 57

Methods

What are the Factors of 57?

The following are the different types of factors of 57:

• Factors of 57: 1, 3, 19, 57

• Sum of Factors of 57: 80

• Negative Factors of 57: -1, -3, -19, -57

• Prime Factors of 57: 3, 19

• Prime Factorization of 57: 3^1 × 19^1

There are two ways to find the factors of 57: using factor pairs, and using prime factorization.

The Factor Pairs of 57

Factor pairs of 57 are any two numbers that, when multiplied together, equal 57. The question to ask is “what two numbers multiplied together equal 57?” Every factor can be paired with another factor, and multiplying the two will result in 57.

To find the factor pairs of 57, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 57. 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 3.

Step 2:

Divide 57 by the smallest prime factor, in this case, 3:

57 ÷ 3 = 19

3 and 19 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 19 as the new focus. Find the smallest prime factor that isn’t 1, and divide 19 by that number. In this case, 19 is the new smallest prime factor:

19 ÷ 19 = 1

Remember that this new factor pair is only for the factors of 19, not 57. So, to finish the factor pair for 57, you’d multiply 3 and 19 before pairing with 1:

3 x 19 = 57

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 57:

(1, 57), (3, 19)

So, to list all the factors of 57: 1, 3, 19, 57

The negative factors of 57 would be: -1, -3, -19, -57

Prime Factorization of 57

To find the Prime factorization of 57, we break down all the factors of 57 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 57 only has a few differences from the above method of finding the factors of 57. 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 57:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 57. 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 3.

Step 2:

Divide 57 by the smallest prime factor, in this case, 3

57 ÷ 3 = 19

3 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 19 as the new focus. Find the smallest prime factor that isn’t 1, and divide 19 by that number. The smallest prime factor you pick for 19 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 57 are: 3, 19

Find the Factors of Other Numbers

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

Factors of 88 - The factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88

Factors of 4 - The factors of 4 are 1, 2, 4

Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 68 - The factors of 68 are 1, 2, 4, 17, 34, 68

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

Get PDF

Your Child Can Improve Their Math Scores By 90% Within 3 months!

Our elite math tutors are ready to help make your child a math champion! Sign up for our zero $ free trial to get started today.

Start Zero $ 7-Day Trial