What are the Factors of 12?

The following are the different types of factors of 12:

• Factors of 12: 1, 2, 3, 4, 6, 12

• Sum of Factors of 12: 28

• Negative Factors of 12: -1, -2, -3, -4, -6, -12

• Prime Factors of 12: 2, 3

• Prime Factorization of 12: 2^2 × 3^1

There are two ways to find the factors of 12: using factor pairs, and using prime factorization.

Factor pairs of 12 are any two numbers that, when multiplied together, equal 12. The question to ask is “what two numbers multiplied together equal 12?” Every factor can be paired with another factor, and multiplying the two will result in 12.

To find the factor pairs of 12, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 12. 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 12 by the smallest prime factor, in this case, 2:

12 ÷ 2 = 6

2 and 6 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 6 as the new focus. Find the smallest prime factor that isn’t 1, and divide 6 by that number. In this case, 2 is the new smallest prime factor:

6 ÷ 2 = 3

Remember that this new factor pair is only for the factors of 6, not 12. So, to finish the factor pair for 12, you’d multiply 2 and 2 before pairing with 3:

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 12:

(1, 12), (2, 6), (3, 4)

So, to list all the factors of 12: 1, 2, 3, 4, 6, 12

The negative factors of 12 would be: -1, -2, -3, -4, -6, -12

To find the Prime factorization of 12, we break down all the factors of 12 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 12 only has a few differences from the above method of finding the factors of 12. 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 12:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 12. 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 12 by the smallest prime factor, in this case, 2

12 ÷ 2 = 6

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 6 as the new focus. Find the smallest prime factor that isn’t 1, and divide 6 by that number. The smallest prime factor you pick for 6 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 12 are: 2, 3

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

Factors of 35 - The factors of 35 are 1, 5, 7, 35

Factors of 55 - The factors of 55 are 1, 5, 11, 55

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

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