Factor pairs of 1800 are any two numbers that, when multiplied together, equal 1800. The question to ask is “what two numbers multiplied together equal 1800?” Every factor can be paired with another factor, and multiplying the two will result in 1800.
To find the factor pairs of 1800, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1800. 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 1800 by the smallest prime factor, in this case, 2:
1800 ÷ 2 = 900
2 and 900 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 900 as the new focus. Find the smallest prime factor that isn’t 1, and divide 900 by that number. In this case, 2 is the new smallest prime factor:
900 ÷ 2 = 450
Remember that this new factor pair is only for the factors of 900, not 1800. So, to finish the factor pair for 1800, you’d multiply 2 and 2 before pairing with 450:
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 1800:
(1, 1800), (2, 900), (3, 600), (4, 450), (5, 360), (6, 300), (8, 225), (9, 200), (10, 180), (12, 150), (15, 120), (18, 100), (20, 90), (24, 75), (25, 72), (30, 60), (36, 50), (40, 45)
So, to list all the factors of 1800: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800
The negative factors of 1800 would be: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -25, -30, -36, -40, -45, -50, -60, -72, -75, -90, -100, -120, -150, -180, -200, -225, -300, -360, -450, -600, -900, -1800