What are the Factors of 1122?

The following are the different types of factors of 1122:

• Factors of 1122: 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122

• Sum of Factors of 1122: 2592

• Negative Factors of 1122: -1, -2, -3, -6, -11, -17, -22, -33, -34, -51, -66, -102, -187, -374, -561, -1122

• Prime Factors of 1122: 2, 3, 11, 17

• Prime Factorization of 1122: 2^1 × 3^1 × 11^1 × 17^1

There are two ways to find the factors of 1122: using factor pairs, and using prime factorization.

Factor pairs of 1122 are any two numbers that, when multiplied together, equal 1122. The question to ask is “what two numbers multiplied together equal 1122?” Every factor can be paired with another factor, and multiplying the two will result in 1122.

To find the factor pairs of 1122, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1122. 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 1122 by the smallest prime factor, in this case, 2:

1122 ÷ 2 = 561

2 and 561 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 561 as the new focus. Find the smallest prime factor that isn’t 1, and divide 561 by that number. In this case, 3 is the new smallest prime factor:

561 ÷ 3 = 187

Remember that this new factor pair is only for the factors of 561, not 1122. So, to finish the factor pair for 1122, you’d multiply 2 and 3 before pairing with 187:

2 x 3 = 6

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 1122:

(1, 1122), (2, 561), (3, 374), (6, 187), (11, 102), (17, 66), (22, 51), (33, 34)

So, to list all the factors of 1122: 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122

The negative factors of 1122 would be: -1, -2, -3, -6, -11, -17, -22, -33, -34, -51, -66, -102, -187, -374, -561, -1122

To find the Prime factorization of 1122, we break down all the factors of 1122 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 1122 only has a few differences from the above method of finding the factors of 1122. 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 1122:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1122. 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 1122 by the smallest prime factor, in this case, 2

1122 ÷ 2 = 561

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 561 as the new focus. Find the smallest prime factor that isn’t 1, and divide 561 by that number. The smallest prime factor you pick for 561 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 1122 are: 2, 3, 11, 17

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

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

Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

Factors of 117 - The factors of 117 are 1, 3, 9, 13, 39, 117

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