Factor pairs of 378 are any two numbers that, when multiplied together, equal 378. The question to ask is “what two numbers multiplied together equal 378?” Every factor can be paired with another factor, and multiplying the two will result in 378.
To find the factor pairs of 378, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 378. 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 378 by the smallest prime factor, in this case, 2:
378 ÷ 2 = 189
2 and 189 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 189 as the new focus. Find the smallest prime factor that isn’t 1, and divide 189 by that number. In this case, 3 is the new smallest prime factor:
189 ÷ 3 = 63
Remember that this new factor pair is only for the factors of 189, not 378. So, to finish the factor pair for 378, you’d multiply 2 and 3 before pairing with 63:
2 x 3 = 6
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 378:
(1, 378), (2, 189), (3, 126), (6, 63), (7, 54), (9, 42), (14, 27), (18, 21)
So, to list all the factors of 378: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The negative factors of 378 would be: -1, -2, -3, -6, -7, -9, -14, -18, -21, -27, -42, -54, -63, -126, -189, -378