Factor pairs of 242 are any two numbers that, when multiplied together, equal 242. The question to ask is “what two numbers multiplied together equal 242?” Every factor can be paired with another factor, and multiplying the two will result in 242.
To find the factor pairs of 242, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 242. 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 242 by the smallest prime factor, in this case, 2:
242 ÷ 2 = 121
2 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 242. So, to finish the factor pair for 242, you’d multiply 2 and 11 before pairing with 11:
2 x 11 = 22
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 242:
(1, 242), (2, 121), (11, 22)
So, to list all the factors of 242: 1, 2, 11, 22, 121, 242
The negative factors of 242 would be: -1, -2, -11, -22, -121, -242