Factor pairs of 102 are any two numbers that, when multiplied together, equal 102. The question to ask is “what two numbers multiplied together equal 102?” Every factor can be paired with another factor, and multiplying the two will result in 102.

To find the factor pairs of 102, follow these steps:

**Step 1:**

Find the smallest prime number that is larger than 1, and is a factor of 102. 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 102 by the smallest prime factor, in this case, 2:

102 ÷ 2 = 51

2 and 51 will make a new factor pair.

**Step 3:**

Repeat Steps 1 and 2, using 51 as the new focus. Find the smallest prime factor that isn’t 1, and divide 51 by that number. In this case, 3 is the new smallest prime factor:

51 ÷ 3 = 17

Remember that this new factor pair is only for the factors of 51, not 102. So, to finish the factor pair for 102, you’d multiply 2 and 3 before pairing with 17:

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 102:

(1, 102), (2, 51), (3, 34), (6, 17)

So, to list all the factors of 102: 1, 2, 3, 6, 17, 34, 51, 102

The negative factors of 102 would be: -1, -2, -3, -6, -17, -34, -51, -102