Factor pairs of 5184 are any two numbers that, when multiplied together, equal 5184. The question to ask is “what two numbers multiplied together equal 5184?” Every factor can be paired with another factor, and multiplying the two will result in 5184.
To find the factor pairs of 5184, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 5184. 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 5184 by the smallest prime factor, in this case, 2:
5184 ÷ 2 = 2592
2 and 2592 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 2592 as the new focus. Find the smallest prime factor that isn’t 1, and divide 2592 by that number. In this case, 2 is the new smallest prime factor:
2592 ÷ 2 = 1296
Remember that this new factor pair is only for the factors of 2592, not 5184. So, to finish the factor pair for 5184, you’d multiply 2 and 2 before pairing with 1296:
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 5184:
(1, 5184), (2, 2592), (3, 1728), (4, 1296), (6, 864), (8, 648), (9, 576), (12, 432), (16, 324), (18, 288), (24, 216), (27, 192), (32, 162), (36, 144), (48, 108), (54, 96), (64, 81), (72, 72)
So, to list all the factors of 5184: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184
The negative factors of 5184 would be: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -64, -72, -81, -96, -108, -144, -162, -192, -216, -288, -324, -432, -576, -648, -864, -1296, -1728, -2592, -5184