Factor pairs of 2401 are any two numbers that, when multiplied together, equal 2401. The question to ask is “what two numbers multiplied together equal 2401?” Every factor can be paired with another factor, and multiplying the two will result in 2401.
To find the factor pairs of 2401, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 2401. 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 7.
Step 2:
Divide 2401 by the smallest prime factor, in this case, 7:
2401 ÷ 7 = 343
7 and 343 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 343 as the new focus. Find the smallest prime factor that isn’t 1, and divide 343 by that number. In this case, 7 is the new smallest prime factor:
343 ÷ 7 = 49
Remember that this new factor pair is only for the factors of 343, not 2401. So, to finish the factor pair for 2401, you’d multiply 7 and 7 before pairing with 49:
7 x 7 = 49
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 2401:
(1, 2401), (7, 343), (49, 49)
So, to list all the factors of 2401: 1, 7, 49, 343, 2401
The negative factors of 2401 would be: -1, -7, -49, -343, -2401