Q: What are the factor combinations of the number 147,407?

 A:
Positive:   1 x 14740713 x 1133917 x 867123 x 640929 x 5083221 x 667299 x 493377 x 391
Negative: -1 x -147407-13 x -11339-17 x -8671-23 x -6409-29 x -5083-221 x -667-299 x -493-377 x -391


How do I find the factor combinations of the number 147,407?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 147,407, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 147,407
-1 -147,407

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 147,407.

Example:
1 x 147,407 = 147,407
and
-1 x -147,407 = 147,407
Notice both answers equal 147,407

With that explanation out of the way, let's continue. Next, we take the number 147,407 and divide it by 2:

147,407 ÷ 2 = 73,703.5

If the quotient is a whole number, then 2 and 73,703.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 147,407
-1 -147,407

Now, we try dividing 147,407 by 3:

147,407 ÷ 3 = 49,135.6667

If the quotient is a whole number, then 3 and 49,135.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 147,407
-1 -147,407

Let's try dividing by 4:

147,407 ÷ 4 = 36,851.75

If the quotient is a whole number, then 4 and 36,851.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 147,407
-1 147,407
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

1131723292212993773914936675,0836,4098,67111,339147,407
-1-13-17-23-29-221-299-377-391-493-667-5,083-6,409-8,671-11,339-147,407

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