Q: What are the factor combinations of the number 42,605,641?

 A:
Positive:   1 x 4260564113 x 327735747 x 906503103 x 413647611 x 69731677 x 629331339 x 318194841 x 8801
Negative: -1 x -42605641-13 x -3277357-47 x -906503-103 x -413647-611 x -69731-677 x -62933-1339 x -31819-4841 x -8801


How do I find the factor combinations of the number 42,605,641?

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 42,605,641, 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 42,605,641
-1 -42,605,641

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 42,605,641.

Example:
1 x 42,605,641 = 42,605,641
and
-1 x -42,605,641 = 42,605,641
Notice both answers equal 42,605,641

With that explanation out of the way, let's continue. Next, we take the number 42,605,641 and divide it by 2:

42,605,641 ÷ 2 = 21,302,820.5

If the quotient is a whole number, then 2 and 21,302,820.5 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 42,605,641
-1 -42,605,641

Now, we try dividing 42,605,641 by 3:

42,605,641 ÷ 3 = 14,201,880.3333

If the quotient is a whole number, then 3 and 14,201,880.3333 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 42,605,641
-1 -42,605,641

Let's try dividing by 4:

42,605,641 ÷ 4 = 10,651,410.25

If the quotient is a whole number, then 4 and 10,651,410.25 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 42,605,641
-1 42,605,641
Keep dividing by the next highest number until you cannot divide anymore.

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

113471036116771,3394,8418,80131,81962,93369,731413,647906,5033,277,35742,605,641
-1-13-47-103-611-677-1,339-4,841-8,801-31,819-62,933-69,731-413,647-906,503-3,277,357-42,605,641

More Examples

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