Factor pairs of 196 are any two numbers that, when multiplied together, equal 196. The question to ask is “what two numbers multiplied together equal 196?” Every factor can be paired with another factor, and multiplying the two will result in 196.
To find the factor pairs of 196, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 196. 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 196 by the smallest prime factor, in this case, 2:
196 ÷ 2 = 98
2 and 98 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 98 as the new focus. Find the smallest prime factor that isn’t 1, and divide 98 by that number. In this case, 2 is the new smallest prime factor:
98 ÷ 2 = 49
Remember that this new factor pair is only for the factors of 98, not 196. So, to finish the factor pair for 196, you’d multiply 2 and 2 before pairing with 49:
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 196:
(1, 196), (2, 98), (4, 49), (7, 28), (14, 14)
So, to list all the factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, 196
The negative factors of 196 would be: -1, -2, -4, -7, -14, -28, -49, -98, -196