Factor pairs of 672 are any two numbers that, when multiplied together, equal 672. The question to ask is “what two numbers multiplied together equal 672?” Every factor can be paired with another factor, and multiplying the two will result in 672.
To find the factor pairs of 672, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 672. 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 672 by the smallest prime factor, in this case, 2:
672 ÷ 2 = 336
2 and 336 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 336 as the new focus. Find the smallest prime factor that isn’t 1, and divide 336 by that number. In this case, 2 is the new smallest prime factor:
336 ÷ 2 = 168
Remember that this new factor pair is only for the factors of 336, not 672. So, to finish the factor pair for 672, you’d multiply 2 and 2 before pairing with 168:
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 672:
(1, 672), (2, 336), (3, 224), (4, 168), (6, 112), (7, 96), (8, 84), (12, 56), (14, 48), (16, 42), (21, 32), (24, 28)
So, to list all the factors of 672: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672
The negative factors of 672 would be: -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -32, -42, -48, -56, -84, -96, -112, -168, -224, -336, -672