Factor pairs of 57 are any two numbers that, when multiplied together, equal 57. The question to ask is “what two numbers multiplied together equal 57?” Every factor can be paired with another factor, and multiplying the two will result in 57.

To find the factor pairs of 57, follow these steps:

**Step 1:**

Find the smallest prime number that is larger than 1, and is a factor of 57. 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 57 by the smallest prime factor, in this case, 3:

57 ÷ 3 = 19

3 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 57. So, to finish the factor pair for 57, you’d multiply 3 and 19 before pairing with 1:

3 x 19 = 57

**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 57:

(1, 57), (3, 19)

So, to list all the factors of 57: 1, 3, 19, 57

The negative factors of 57 would be: -1, -3, -19, -57