As your math tutor, I’m here to help you break down factor pairs of 567 step by step!
Factor pairs of 567 are any two numbers that, when multiplied together, equal 567. The question to ask is “what two numbers multiplied together equal 567?” Every factor can be paired with another factor, and multiplying the two will result in 567.
To find the factor pairs of 567, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 567. 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 567 by the smallest prime factor, in this case, 3:
567 ÷ 3 = 189
3 and 189 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 189 as the new focus. Find the smallest prime factor that isn’t 1, and divide 189 by that number. In this case, 3 is the new smallest prime factor:
189 ÷ 3 = 63
Remember that this new factor pair is only for the factors of 189, not 567. So, to finish the factor pair for 567, you’d multiply 3 and 3 before pairing with 63:
3 x 3 = 9
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 567:
(1, 567), (3, 189), (7, 81), (9, 63), (21, 27)
So, to list all the factors of 567: 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The negative factors of 567 would be: -1, -3, -7, -9, -21, -27, -63, -81, -189, -567
Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!