Factor pairs of 728 are any two numbers that, when multiplied together, equal 728. The question to ask is “what two numbers multiplied together equal 728?” Every factor can be paired with another factor, and multiplying the two will result in 728.
To find the factor pairs of 728, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 728. 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 728 by the smallest prime factor, in this case, 2:
728 ÷ 2 = 364
2 and 364 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 364 as the new focus. Find the smallest prime factor that isn’t 1, and divide 364 by that number. In this case, 2 is the new smallest prime factor:
364 ÷ 2 = 182
Remember that this new factor pair is only for the factors of 364, not 728. So, to finish the factor pair for 728, you’d multiply 2 and 2 before pairing with 182:
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 728:
(1, 728), (2, 364), (4, 182), (7, 104), (8, 91), (13, 56), (14, 52), (26, 28)
So, to list all the factors of 728: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The negative factors of 728 would be: -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, -728