Factor pairs of 525 are any two numbers that, when multiplied together, equal 525. The question to ask is “what two numbers multiplied together equal 525?” Every factor can be paired with another factor, and multiplying the two will result in 525.
To find the factor pairs of 525, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 525. 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 3.
Step 2:
Divide 525 by the smallest prime factor, in this case, 3:
525 ÷ 3 = 175
3 and 175 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 175 as the new focus. Find the smallest prime factor that isn’t 1, and divide 175 by that number. In this case, 5 is the new smallest prime factor:
175 ÷ 5 = 35
Remember that this new factor pair is only for the factors of 175, not 525. So, to finish the factor pair for 525, you’d multiply 3 and 5 before pairing with 35:
3 x 5 = 15
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 525:
(1, 525), (3, 175), (5, 105), (7, 75), (15, 35), (21, 25)
So, to list all the factors of 525: 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525
The negative factors of 525 would be: -1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -175, -525