Factor pairs of 800 are any two numbers that, when multiplied together, equal 800. The question to ask is “what two numbers multiplied together equal 800?” Every factor can be paired with another factor, and multiplying the two will result in 800.
To find the factor pairs of 800, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 800. 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 800 by the smallest prime factor, in this case, 2:
800 ÷ 2 = 400
2 and 400 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 400 as the new focus. Find the smallest prime factor that isn’t 1, and divide 400 by that number. In this case, 2 is the new smallest prime factor:
400 ÷ 2 = 200
Remember that this new factor pair is only for the factors of 400, not 800. So, to finish the factor pair for 800, you’d multiply 2 and 2 before pairing with 200:
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 800:
(1, 800), (2, 400), (4, 200), (5, 160), (8, 100), (10, 80), (16, 50), (20, 40), (25, 32)
So, to list all the factors of 800: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
The negative factors of 800 would be: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -160, -200, -400, -800