Factor pairs of 363 are any two numbers that, when multiplied together, equal 363. The question to ask is “what two numbers multiplied together equal 363?” Every factor can be paired with another factor, and multiplying the two will result in 363.
To find the factor pairs of 363, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 363. 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 363 by the smallest prime factor, in this case, 3:
363 ÷ 3 = 121
3 and 121 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 121 as the new focus. Find the smallest prime factor that isn’t 1, and divide 121 by that number. In this case, 11 is the new smallest prime factor:
121 ÷ 11 = 11
Remember that this new factor pair is only for the factors of 121, not 363. So, to finish the factor pair for 363, you’d multiply 3 and 11 before pairing with 11:
3 x 11 = 33
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 363:
(1, 363), (3, 121), (11, 33)
So, to list all the factors of 363: 1, 3, 11, 33, 121, 363
The negative factors of 363 would be: -1, -3, -11, -33, -121, -363