Factor pairs of 1000 are any two numbers that, when multiplied together, equal 1000. The question to ask is “what two numbers multiplied together equal 1000?” Every factor can be paired with another factor, and multiplying the two will result in 1000.
To find the factor pairs of 1000, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1000. 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 1000 by the smallest prime factor, in this case, 2:
1000 ÷ 2 = 500
2 and 500 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 500 as the new focus. Find the smallest prime factor that isn’t 1, and divide 500 by that number. In this case, 2 is the new smallest prime factor:
500 ÷ 2 = 250
Remember that this new factor pair is only for the factors of 500, not 1000. So, to finish the factor pair for 1000, you’d multiply 2 and 2 before pairing with 250:
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 1000:
(1, 1000), (2, 500), (4, 250), (5, 200), (8, 125), (10, 100), (20, 50), (25, 40)
So, to list all the factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The negative factors of 1000 would be: -1, -2, -4, -5, -8, -10, -20, -25, -40, -50, -100, -125, -200, -250, -500, -1000