Q: What are the factor combinations of the number 38,657,723?

 A:
Positive:   1 x 3865772313 x 297367119 x 203461753 x 729391247 x 156509689 x 561071007 x 383892953 x 13091
Negative: -1 x -38657723-13 x -2973671-19 x -2034617-53 x -729391-247 x -156509-689 x -56107-1007 x -38389-2953 x -13091


How do I find the factor combinations of the number 38,657,723?

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 38,657,723, 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 38,657,723
-1 -38,657,723

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 38,657,723.

Example:
1 x 38,657,723 = 38,657,723
and
-1 x -38,657,723 = 38,657,723
Notice both answers equal 38,657,723

With that explanation out of the way, let's continue. Next, we take the number 38,657,723 and divide it by 2:

38,657,723 ÷ 2 = 19,328,861.5

If the quotient is a whole number, then 2 and 19,328,861.5 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 38,657,723
-1 -38,657,723

Now, we try dividing 38,657,723 by 3:

38,657,723 ÷ 3 = 12,885,907.6667

If the quotient is a whole number, then 3 and 12,885,907.6667 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 38,657,723
-1 -38,657,723

Let's try dividing by 4:

38,657,723 ÷ 4 = 9,664,430.75

If the quotient is a whole number, then 4 and 9,664,430.75 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 38,657,723
-1 38,657,723
Keep dividing by the next highest number until you cannot divide anymore.

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

11319532476891,0072,95313,09138,38956,107156,509729,3912,034,6172,973,67138,657,723
-1-13-19-53-247-689-1,007-2,953-13,091-38,389-56,107-156,509-729,391-2,034,617-2,973,671-38,657,723

More Examples

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