Factor pairs of 4000 are any two numbers that, when multiplied together, equal 4000. The question to ask is “what two numbers multiplied together equal 4000?” Every factor can be paired with another factor, and multiplying the two will result in 4000.
To find the factor pairs of 4000, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 4000. 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 4000 by the smallest prime factor, in this case, 2:
4000 ÷ 2 = 2000
2 and 2000 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 2000 as the new focus. Find the smallest prime factor that isn’t 1, and divide 2000 by that number. In this case, 2 is the new smallest prime factor:
2000 ÷ 2 = 1000
Remember that this new factor pair is only for the factors of 2000, not 4000. So, to finish the factor pair for 4000, you’d multiply 2 and 2 before pairing with 1000:
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 4000:
(1, 4000), (2, 2000), (4, 1000), (5, 800), (8, 500), (10, 400), (16, 250), (20, 200), (25, 160), (32, 125), (40, 100), (50, 80)
So, to list all the factors of 4000: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000
The negative factors of 4000 would be: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -125, -160, -200, -250, -400, -500, -800, -1000, -2000, -4000