Factor pairs of 1750 are any two numbers that, when multiplied together, equal 1750. The question to ask is “what two numbers multiplied together equal 1750?” Every factor can be paired with another factor, and multiplying the two will result in 1750.
To find the factor pairs of 1750, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1750. 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 1750 by the smallest prime factor, in this case, 2:
1750 ÷ 2 = 875
2 and 875 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 875 as the new focus. Find the smallest prime factor that isn’t 1, and divide 875 by that number. In this case, 5 is the new smallest prime factor:
875 ÷ 5 = 175
Remember that this new factor pair is only for the factors of 875, not 1750. So, to finish the factor pair for 1750, you’d multiply 2 and 5 before pairing with 175:
2 x 5 = 10
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 1750:
(1, 1750), (2, 875), (5, 350), (7, 250), (10, 175), (14, 125), (25, 70), (35, 50)
So, to list all the factors of 1750: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750
The negative factors of 1750 would be: -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -125, -175, -250, -350, -875, -1750