As your math tutor, I’m here to help you break down factor pairs of 240 step by step!
Factor pairs of 240 are any two numbers that, when multiplied together, equal 240. The question to ask is “what two numbers multiplied together equal 240?” Every factor can be paired with another factor, and multiplying the two will result in 240.
To find the factor pairs of 240, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 240. 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 240 by the smallest prime factor, in this case, 2:
240 ÷ 2 = 120
2 and 120 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 120 as the new focus. Find the smallest prime factor that isn’t 1, and divide 120 by that number. In this case, 2 is the new smallest prime factor:
120 ÷ 2 = 60
Remember that this new factor pair is only for the factors of 120, not 240. So, to finish the factor pair for 240, you’d multiply 2 and 2 before pairing with 60:
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 240:
(1, 240), (2, 120), (3, 80), (4, 60), (5, 48), (6, 40), (8, 30), (10, 24), (12, 20), (15, 16)
So, to list all the factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The negative factors of 240 would be: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -40, -48, -60, -80, -120, -240
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!