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