Q: What are the factor combinations of the number 35,424,341?

 A:
Positive:   1 x 3542434119 x 186443929 x 1221529239 x 148219269 x 131689551 x 642914541 x 78015111 x 6931
Negative: -1 x -35424341-19 x -1864439-29 x -1221529-239 x -148219-269 x -131689-551 x -64291-4541 x -7801-5111 x -6931


How do I find the factor combinations of the number 35,424,341?

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 35,424,341, 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 35,424,341
-1 -35,424,341

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 35,424,341.

Example:
1 x 35,424,341 = 35,424,341
and
-1 x -35,424,341 = 35,424,341
Notice both answers equal 35,424,341

With that explanation out of the way, let's continue. Next, we take the number 35,424,341 and divide it by 2:

35,424,341 ÷ 2 = 17,712,170.5

If the quotient is a whole number, then 2 and 17,712,170.5 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 35,424,341
-1 -35,424,341

Now, we try dividing 35,424,341 by 3:

35,424,341 ÷ 3 = 11,808,113.6667

If the quotient is a whole number, then 3 and 11,808,113.6667 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 35,424,341
-1 -35,424,341

Let's try dividing by 4:

35,424,341 ÷ 4 = 8,856,085.25

If the quotient is a whole number, then 4 and 8,856,085.25 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 35,424,341
-1 35,424,341
Keep dividing by the next highest number until you cannot divide anymore.

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

119292392695514,5415,1116,9317,80164,291131,689148,2191,221,5291,864,43935,424,341
-1-19-29-239-269-551-4,541-5,111-6,931-7,801-64,291-131,689-148,219-1,221,529-1,864,439-35,424,341

More Examples

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