Factor pairs of 1296 are any two numbers that, when multiplied together, equal 1296. The question to ask is “what two numbers multiplied together equal 1296?” Every factor can be paired with another factor, and multiplying the two will result in 1296.
To find the factor pairs of 1296, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1296. 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 1296 by the smallest prime factor, in this case, 2:
1296 ÷ 2 = 648
2 and 648 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 648 as the new focus. Find the smallest prime factor that isn’t 1, and divide 648 by that number. In this case, 2 is the new smallest prime factor:
648 ÷ 2 = 324
Remember that this new factor pair is only for the factors of 648, not 1296. So, to finish the factor pair for 1296, you’d multiply 2 and 2 before pairing with 324:
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 1296:
(1, 1296), (2, 648), (3, 432), (4, 324), (6, 216), (8, 162), (9, 144), (12, 108), (16, 81), (18, 72), (24, 54), (27, 48), (36, 36)
So, to list all the factors of 1296: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296
The negative factors of 1296 would be: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -36, -48, -54, -72, -81, -108, -144, -162, -216, -324, -432, -648, -1296