Factor pairs of 768 are any two numbers that, when multiplied together, equal 768. The question to ask is “what two numbers multiplied together equal 768?” Every factor can be paired with another factor, and multiplying the two will result in 768.
To find the factor pairs of 768, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 768. 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 768 by the smallest prime factor, in this case, 2:
768 ÷ 2 = 384
2 and 384 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 384 as the new focus. Find the smallest prime factor that isn’t 1, and divide 384 by that number. In this case, 2 is the new smallest prime factor:
384 ÷ 2 = 192
Remember that this new factor pair is only for the factors of 384, not 768. So, to finish the factor pair for 768, you’d multiply 2 and 2 before pairing with 192:
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 768:
(1, 768), (2, 384), (3, 256), (4, 192), (6, 128), (8, 96), (12, 64), (16, 48), (24, 32)
So, to list all the factors of 768: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The negative factors of 768 would be: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -128, -192, -256, -384, -768