Factor pairs of 156 are any two numbers that, when multiplied together, equal 156. The question to ask is “what two numbers multiplied together equal 156?” Every factor can be paired with another factor, and multiplying the two will result in 156.
To find the factor pairs of 156, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 156. 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 156 by the smallest prime factor, in this case, 2:
156 ÷ 2 = 78
2 and 78 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 78 as the new focus. Find the smallest prime factor that isn’t 1, and divide 78 by that number. In this case, 2 is the new smallest prime factor:
78 ÷ 2 = 39
Remember that this new factor pair is only for the factors of 78, not 156. So, to finish the factor pair for 156, you’d multiply 2 and 2 before pairing with 39:
2 x 2 = 4
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 156:
(1, 156), (2, 78), (3, 52), (4, 39), (6, 26), (12, 13)
So, to list all the factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The negative factors of 156 would be: -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, -156