What are the Factors of 10?

Factors of 10 are any integer that can be multiplied by another integer to make exactly 10. In other words, finding the factors of 10 is like breaking down the number 10 into all the smaller pieces that can be used in a multiplication problem to equal 10.

Factors of 10

Methods

What are the Factors of 10?

The following are the different types of factors of 10:

• Factors of 10: 1, 2, 5, 10

• Sum of Factors of 10: 18

• Negative Factors of 10: -1, -2, -5, -10

• Prime Factors of 10: 2, 5

• Prime Factorization of 10: 2^1 × 5^1

There are two ways to find the factors of 10: using factor pairs, and using prime factorization.

The Factor Pairs of 10

Factor pairs of 10 are any two numbers that, when multiplied together, equal 10. The question to ask is “what two numbers multiplied together equal 10?” Every factor can be paired with another factor, and multiplying the two will result in 10.

To find the factor pairs of 10, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 10. 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 10 by the smallest prime factor, in this case, 2:

10 ÷ 2 = 5

2 and 5 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 5 as the new focus. Find the smallest prime factor that isn’t 1, and divide 5 by that number. In this case, 5 is the new smallest prime factor:

5 ÷ 5 = 1

Remember that this new factor pair is only for the factors of 5, not 10. So, to finish the factor pair for 10, you’d multiply 2 and 5 before pairing with 1:

2 x 5 = 10

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 10:

(1, 10), (2, 5)

So, to list all the factors of 10: 1, 2, 5, 10

The negative factors of 10 would be: -1, -2, -5, -10

Prime Factorization of 10

To find the Prime factorization of 10, we break down all the factors of 10 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 10 only has a few differences from the above method of finding the factors of 10. 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 10:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 10. 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 10 by the smallest prime factor, in this case, 2

10 ÷ 2 = 5

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 5 as the new focus. Find the smallest prime factor that isn’t 1, and divide 5 by that number. The smallest prime factor you pick for 5 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 10 are: 2, 5

Find the Factors of Other Numbers

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

Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

Factors of 15 - The factors of 15 are 1, 3, 5, 15

Factors of 109 - The factors of 109 are 1, 109

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

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