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