As your math tutor, I’m here to help you break down factor pairs of 204 step by step!
Factor pairs of 204 are any two numbers that, when multiplied together, equal 204. The question to ask is “what two numbers multiplied together equal 204?” Every factor can be paired with another factor, and multiplying the two will result in 204.
To find the factor pairs of 204, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 204. 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 204 by the smallest prime factor, in this case, 2:
204 ÷ 2 = 102
2 and 102 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 102 as the new focus. Find the smallest prime factor that isn’t 1, and divide 102 by that number. In this case, 2 is the new smallest prime factor:
102 ÷ 2 = 51
Remember that this new factor pair is only for the factors of 102, not 204. So, to finish the factor pair for 204, you’d multiply 2 and 2 before pairing with 51:
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 204:
(1, 204), (2, 102), (3, 68), (4, 51), (6, 34), (12, 17)
So, to list all the factors of 204: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The negative factors of 204 would be: -1, -2, -3, -4, -6, -12, -17, -34, -51, -68, -102, -204
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!