What are the Factors of 361?

The following are the different types of factors of 361:

• Factors of 361: 1, 19, 361

• Sum of Factors of 361: 381

• Negative Factors of 361: -1, -19, -361

• Prime Factors of 361: 19

• Prime Factorization of 361: 19^2

There are two ways to find the factors of 361: using factor pairs, and using prime factorization.

Factor pairs of 361 are any two numbers that, when multiplied together, equal 361. The question to ask is “what two numbers multiplied together equal 361?” Every factor can be paired with another factor, and multiplying the two will result in 361.

To find the factor pairs of 361, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 361. 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 19.

Step 2:

Divide 361 by the smallest prime factor, in this case, 19:

361 ÷ 19 = 19

19 and 19 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 19 as the new focus. Find the smallest prime factor that isn’t 1, and divide 19 by that number. In this case, 19 is the new smallest prime factor:

19 ÷ 19 = 1

Remember that this new factor pair is only for the factors of 19, not 361. So, to finish the factor pair for 361, you’d multiply 19 and 19 before pairing with 1:

19 x 19 = 361

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 361:

(1, 361), (19, 19)

So, to list all the factors of 361: 1, 19, 361

The negative factors of 361 would be: -1, -19, -361

To find the Prime factorization of 361, we break down all the factors of 361 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 361 only has a few differences from the above method of finding the factors of 361. 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 361:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 361. 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 19.

Step 2:

Divide 361 by the smallest prime factor, in this case, 19

361 ÷ 19 = 19

19 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 19 as the new focus. Find the smallest prime factor that isn’t 1, and divide 19 by that number. The smallest prime factor you pick for 19 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 361 are: 19

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

Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

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

Factors of 77 - The factors of 77 are 1, 7, 11, 77

Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96