What are the Factors of 52?

The following are the different types of factors of 52:

• Factors of 52: 1, 2, 4, 13, 26, 52

• Sum of Factors of 52: 98

• Negative Factors of 52: -1, -2, -4, -13, -26, -52

• Prime Factors of 52: 2, 13

• Prime Factorization of 52: 2^2 × 13^1

There are two ways to find the factors of 52: using factor pairs, and using prime factorization.

Factor pairs of 52 are any two numbers that, when multiplied together, equal 52. The question to ask is “what two numbers multiplied together equal 52?” Every factor can be paired with another factor, and multiplying the two will result in 52.

To find the factor pairs of 52, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 52. 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 52 by the smallest prime factor, in this case, 2:

52 ÷ 2 = 26

2 and 26 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 26 as the new focus. Find the smallest prime factor that isn’t 1, and divide 26 by that number. In this case, 2 is the new smallest prime factor:

26 ÷ 2 = 13

Remember that this new factor pair is only for the factors of 26, not 52. So, to finish the factor pair for 52, you’d multiply 2 and 2 before pairing with 13:

2 x 2 = 4

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 52:

(1, 52), (2, 26), (4, 13)

So, to list all the factors of 52: 1, 2, 4, 13, 26, 52

The negative factors of 52 would be: -1, -2, -4, -13, -26, -52

To find the Prime factorization of 52, we break down all the factors of 52 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 52 only has a few differences from the above method of finding the factors of 52. 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 52:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 52. 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 52 by the smallest prime factor, in this case, 2

52 ÷ 2 = 26

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 26 as the new focus. Find the smallest prime factor that isn’t 1, and divide 26 by that number. The smallest prime factor you pick for 26 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 52 are: 2, 13

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

Factors of 147 - The factors of 147 are 1, 3, 7, 21, 49, 147

Factors of 91 - The factors of 91 are 1, 7, 13, 91

Factors of 111 - The factors of 111 are 1, 3, 37, 111

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