As your math tutor, I’m here to help you break down factor pairs of 1024 step by step!
Factor pairs of 1024 are any two numbers that, when multiplied together, equal 1024. The question to ask is “what two numbers multiplied together equal 1024?” Every factor can be paired with another factor, and multiplying the two will result in 1024.
To find the factor pairs of 1024, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1024. 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 1024 by the smallest prime factor, in this case, 2:
1024 ÷ 2 = 512
2 and 512 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 512 as the new focus. Find the smallest prime factor that isn’t 1, and divide 512 by that number. In this case, 2 is the new smallest prime factor:
512 ÷ 2 = 256
Remember that this new factor pair is only for the factors of 512, not 1024. So, to finish the factor pair for 1024, you’d multiply 2 and 2 before pairing with 256:
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 1024:
(1, 1024), (2, 512), (4, 256), (8, 128), (16, 64), (32, 32)
So, to list all the factors of 1024: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
The negative factors of 1024 would be: -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024
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!