Factor pairs of 945 are any two numbers that, when multiplied together, equal 945. The question to ask is “what two numbers multiplied together equal 945?” Every factor can be paired with another factor, and multiplying the two will result in 945.
To find the factor pairs of 945, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 945. 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 3.
Step 2:
Divide 945 by the smallest prime factor, in this case, 3:
945 ÷ 3 = 315
3 and 315 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 315 as the new focus. Find the smallest prime factor that isn’t 1, and divide 315 by that number. In this case, 3 is the new smallest prime factor:
315 ÷ 3 = 105
Remember that this new factor pair is only for the factors of 315, not 945. So, to finish the factor pair for 945, you’d multiply 3 and 3 before pairing with 105:
3 x 3 = 9
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 945:
(1, 945), (3, 315), (5, 189), (7, 135), (9, 105), (15, 63), (21, 45), (27, 35)
So, to list all the factors of 945: 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The negative factors of 945 would be: -1, -3, -5, -7, -9, -15, -21, -27, -35, -45, -63, -105, -135, -189, -315, -945