Factor pairs of 259 are any two numbers that, when multiplied together, equal 259. The question to ask is “what two numbers multiplied together equal 259?” Every factor can be paired with another factor, and multiplying the two will result in 259.
To find the factor pairs of 259, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 259. 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 7.
Step 2:
Divide 259 by the smallest prime factor, in this case, 7:
259 ÷ 7 = 37
7 and 37 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 37 as the new focus. Find the smallest prime factor that isn’t 1, and divide 37 by that number. In this case, 37 is the new smallest prime factor:
37 ÷ 37 = 1
Remember that this new factor pair is only for the factors of 37, not 259. So, to finish the factor pair for 259, you’d multiply 7 and 37 before pairing with 1:
7 x 37 = 259
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 259:
(1, 259), (7, 37)
So, to list all the factors of 259: 1, 7, 37, 259
The negative factors of 259 would be: -1, -7, -37, -259