Factor pairs of 468 are any two numbers that, when multiplied together, equal 468. The question to ask is “what two numbers multiplied together equal 468?” Every factor can be paired with another factor, and multiplying the two will result in 468.
To find the factor pairs of 468, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 468. 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 468 by the smallest prime factor, in this case, 2:
468 ÷ 2 = 234
2 and 234 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 234 as the new focus. Find the smallest prime factor that isn’t 1, and divide 234 by that number. In this case, 2 is the new smallest prime factor:
234 ÷ 2 = 117
Remember that this new factor pair is only for the factors of 234, not 468. So, to finish the factor pair for 468, you’d multiply 2 and 2 before pairing with 117:
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 468:
(1, 468), (2, 234), (3, 156), (4, 117), (6, 78), (9, 52), (12, 39), (13, 36), (18, 26)
So, to list all the factors of 468: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The negative factors of 468 would be: -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, -468