Q: What are the factor combinations of the number 40,302,353?

 A:
Positive:   1 x 403023537 x 575747913 x 310018149 x 82249791 x 442883151 x 266903419 x 96187637 x 632691057 x 381291963 x 205312933 x 137415447 x 7399
Negative: -1 x -40302353-7 x -5757479-13 x -3100181-49 x -822497-91 x -442883-151 x -266903-419 x -96187-637 x -63269-1057 x -38129-1963 x -20531-2933 x -13741-5447 x -7399


How do I find the factor combinations of the number 40,302,353?

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 40,302,353, 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 40,302,353
-1 -40,302,353

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 40,302,353.

Example:
1 x 40,302,353 = 40,302,353
and
-1 x -40,302,353 = 40,302,353
Notice both answers equal 40,302,353

With that explanation out of the way, let's continue. Next, we take the number 40,302,353 and divide it by 2:

40,302,353 ÷ 2 = 20,151,176.5

If the quotient is a whole number, then 2 and 20,151,176.5 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 40,302,353
-1 -40,302,353

Now, we try dividing 40,302,353 by 3:

40,302,353 ÷ 3 = 13,434,117.6667

If the quotient is a whole number, then 3 and 13,434,117.6667 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 40,302,353
-1 -40,302,353

Let's try dividing by 4:

40,302,353 ÷ 4 = 10,075,588.25

If the quotient is a whole number, then 4 and 10,075,588.25 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 40,302,353
-1 40,302,353
Keep dividing by the next highest number until you cannot divide anymore.

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

171349911514196371,0571,9632,9335,4477,39913,74120,53138,12963,26996,187266,903442,883822,4973,100,1815,757,47940,302,353
-1-7-13-49-91-151-419-637-1,057-1,963-2,933-5,447-7,399-13,741-20,531-38,129-63,269-96,187-266,903-442,883-822,497-3,100,181-5,757,479-40,302,353

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