Factor pairs of 273 are any two numbers that, when multiplied together, equal 273. The question to ask is “what two numbers multiplied together equal 273?” Every factor can be paired with another factor, and multiplying the two will result in 273.
To find the factor pairs of 273, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 273. 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 273 by the smallest prime factor, in this case, 3:
273 ÷ 3 = 91
3 and 91 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 91 as the new focus. Find the smallest prime factor that isn’t 1, and divide 91 by that number. In this case, 7 is the new smallest prime factor:
91 ÷ 7 = 13
Remember that this new factor pair is only for the factors of 91, not 273. So, to finish the factor pair for 273, you’d multiply 3 and 7 before pairing with 13:
3 x 7 = 21
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 273:
(1, 273), (3, 91), (7, 39), (13, 21)
So, to list all the factors of 273: 1, 3, 7, 13, 21, 39, 91, 273
The negative factors of 273 would be: -1, -3, -7, -13, -21, -39, -91, -273