What are the Factors of 189?

The following are the different types of factors of 189:

• Factors of 189: 1, 3, 7, 9, 21, 27, 63, 189

• Sum of Factors of 189: 320

• Negative Factors of 189: -1, -3, -7, -9, -21, -27, -63, -189

• Prime Factors of 189: 3, 7

• Prime Factorization of 189: 3^3 × 7^1

There are two ways to find the factors of 189: using factor pairs, and using prime factorization.

Factor pairs of 189 are any two numbers that, when multiplied together, equal 189. The question to ask is “what two numbers multiplied together equal 189?” Every factor can be paired with another factor, and multiplying the two will result in 189.

To find the factor pairs of 189, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 189. 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 189 by the smallest prime factor, in this case, 3:

189 ÷ 3 = 63

3 and 63 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 63 as the new focus. Find the smallest prime factor that isn’t 1, and divide 63 by that number. In this case, 3 is the new smallest prime factor:

63 ÷ 3 = 21

Remember that this new factor pair is only for the factors of 63, not 189. So, to finish the factor pair for 189, you’d multiply 3 and 3 before pairing with 21:

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 189:

(1, 189), (3, 63), (7, 27), (9, 21)

So, to list all the factors of 189: 1, 3, 7, 9, 21, 27, 63, 189

The negative factors of 189 would be: -1, -3, -7, -9, -21, -27, -63, -189

To find the Prime factorization of 189, we break down all the factors of 189 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 189 only has a few differences from the above method of finding the factors of 189. 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 189:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 189. 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 189 by the smallest prime factor, in this case, 3

189 ÷ 3 = 63

3 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 63 as the new focus. Find the smallest prime factor that isn’t 1, and divide 63 by that number. The smallest prime factor you pick for 63 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 189 are: 3, 7

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

Factors of 57 - The factors of 57 are 1, 3, 19, 57

Factors of 116 - The factors of 116 are 1, 2, 4, 29, 58, 116

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

Factors of 123 - The factors of 123 are 1, 3, 41, 123