What are the Factors of 9?

The following are the different types of factors of 9:

• Factors of 9: 1, 3, 9

• Sum of Factors of 9: 13

• Negative Factors of 9: -1, -3, -9

• Prime Factors of 9: 3

• Prime Factorization of 9: 3^2

There are two ways to find the factors of 9: using factor pairs, and using prime factorization.

Factor pairs of 9 are any two numbers that, when multiplied together, equal 9. The question to ask is “what two numbers multiplied together equal 9?” Every factor can be paired with another factor, and multiplying the two will result in 9.

To find the factor pairs of 9, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 9. 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 9 by the smallest prime factor, in this case, 3:

9 ÷ 3 = 3

3 and 3 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 3 as the new focus. Find the smallest prime factor that isn’t 1, and divide 3 by that number. In this case, 3 is the new smallest prime factor:

3 ÷ 3 = 1

Remember that this new factor pair is only for the factors of 3, not 9. So, to finish the factor pair for 9, you’d multiply 3 and 3 before pairing with 1:

3 x 3 = 9

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 9:

(1, 9), (3, 3)

So, to list all the factors of 9: 1, 3, 9

The negative factors of 9 would be: -1, -3, -9

To find the Prime factorization of 9, we break down all the factors of 9 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 9 only has a few differences from the above method of finding the factors of 9. 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 9:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 9. 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 9 by the smallest prime factor, in this case, 3

9 ÷ 3 = 3

3 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 3 as the new focus. Find the smallest prime factor that isn’t 1, and divide 3 by that number. The smallest prime factor you pick for 3 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 9 are: 3

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

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

Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28

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

Factors of 19 - The factors of 19 are 1, 19