As your math tutor, I’m here to help you break down factor pairs of 2278 step by step!
Factor pairs of 2278 are any two numbers that, when multiplied together, equal 2278. The question to ask is “what two numbers multiplied together equal 2278?” Every factor can be paired with another factor, and multiplying the two will result in 2278.
To find the factor pairs of 2278, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 2278. 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 2278 by the smallest prime factor, in this case, 2:
2278 ÷ 2 = 1139
2 and 1139 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 1139 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1139 by that number. In this case, 17 is the new smallest prime factor:
1139 ÷ 17 = 67
Remember that this new factor pair is only for the factors of 1139, not 2278. So, to finish the factor pair for 2278, you’d multiply 2 and 17 before pairing with 67:
2 x 17 = 34
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 2278:
(1, 2278), (2, 1139), (17, 134), (34, 67)
So, to list all the factors of 2278: 1, 2, 17, 34, 67, 134, 1139, 2278
The negative factors of 2278 would be: -1, -2, -17, -34, -67, -134, -1139, -2278
Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!