Factor pairs of 360 are any two numbers that, when multiplied together, equal 360. The question to ask is “what two numbers multiplied together equal 360?” Every factor can be paired with another factor, and multiplying the two will result in 360.
To find the factor pairs of 360, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 360. 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 360 by the smallest prime factor, in this case, 2:
360 ÷ 2 = 180
2 and 180 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 180 as the new focus. Find the smallest prime factor that isn’t 1, and divide 180 by that number. In this case, 2 is the new smallest prime factor:
180 ÷ 2 = 90
Remember that this new factor pair is only for the factors of 180, not 360. So, to finish the factor pair for 360, you’d multiply 2 and 2 before pairing with 90:
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 360:
(1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), (18, 20)
So, to list all the factors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The negative factors of 360 would be: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -30, -36, -40, -45, -60, -72, -90, -120, -180, -360