Factor pairs of 504 are any two numbers that, when multiplied together, equal 504. The question to ask is “what two numbers multiplied together equal 504?” Every factor can be paired with another factor, and multiplying the two will result in 504.
To find the factor pairs of 504, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 504. 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 504 by the smallest prime factor, in this case, 2:
504 ÷ 2 = 252
2 and 252 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 252 as the new focus. Find the smallest prime factor that isn’t 1, and divide 252 by that number. In this case, 2 is the new smallest prime factor:
252 ÷ 2 = 126
Remember that this new factor pair is only for the factors of 252, not 504. So, to finish the factor pair for 504, you’d multiply 2 and 2 before pairing with 126:
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 504:
(1, 504), (2, 252), (3, 168), (4, 126), (6, 84), (7, 72), (8, 63), (9, 56), (12, 42), (14, 36), (18, 28), (21, 24)
So, to list all the factors of 504: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The negative factors of 504 would be: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -56, -63, -72, -84, -126, -168, -252, -504