Factor pairs of 30 are any two numbers that, when multiplied together, equal 30. The question to ask is “what two numbers multiplied together equal 30?” Every factor can be paired with another factor, and multiplying the two will result in 30.
To find the factor pairs of 30, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 30. 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 30 by the smallest prime factor, in this case, 2:
30 ÷ 2 = 15
2 and 15 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 15 as the new focus. Find the smallest prime factor that isn’t 1, and divide 15 by that number. In this case, 3 is the new smallest prime factor:
15 ÷ 3 = 5
Remember that this new factor pair is only for the factors of 15, not 30. So, to finish the factor pair for 30, you’d multiply 2 and 3 before pairing with 5:
2 x 3 = 6
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 30:
(1, 30), (2, 15), (3, 10), (5, 6)
So, to list all the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The negative factors of 30 would be: -1, -2, -3, -5, -6, -10, -15, -30