Factor pairs of 490 are any two numbers that, when multiplied together, equal 490. The question to ask is “what two numbers multiplied together equal 490?” Every factor can be paired with another factor, and multiplying the two will result in 490.
To find the factor pairs of 490, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 490. 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 490 by the smallest prime factor, in this case, 2:
490 ÷ 2 = 245
2 and 245 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 245 as the new focus. Find the smallest prime factor that isn’t 1, and divide 245 by that number. In this case, 5 is the new smallest prime factor:
245 ÷ 5 = 49
Remember that this new factor pair is only for the factors of 245, not 490. So, to finish the factor pair for 490, you’d multiply 2 and 5 before pairing with 49:
2 x 5 = 10
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 490:
(1, 490), (2, 245), (5, 98), (7, 70), (10, 49), (14, 35)
So, to list all the factors of 490: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The negative factors of 490 would be: -1, -2, -5, -7, -10, -14, -35, -49, -70, -98, -245, -490