Q: What are the factor combinations of the number 168,735,749?

 A:
Positive:   1 x 1687357497 x 2410510713 x 1297967391 x 1854239521 x 3238693559 x 474113647 x 462676773 x 24913
Negative: -1 x -168735749-7 x -24105107-13 x -12979673-91 x -1854239-521 x -323869-3559 x -47411-3647 x -46267-6773 x -24913


How do I find the factor combinations of the number 168,735,749?

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 168,735,749, 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.

1 168,735,749
-1 -168,735,749

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 168,735,749.

Example:
1 x 168,735,749 = 168,735,749
and
-1 x -168,735,749 = 168,735,749
Notice both answers equal 168,735,749

With that explanation out of the way, let's continue. Next, we take the number 168,735,749 and divide it by 2:

168,735,749 ÷ 2 = 84,367,874.5

If the quotient is a whole number, then 2 and 84,367,874.5 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:

1 168,735,749
-1 -168,735,749

Now, we try dividing 168,735,749 by 3:

168,735,749 ÷ 3 = 56,245,249.6667

If the quotient is a whole number, then 3 and 56,245,249.6667 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:

1 168,735,749
-1 -168,735,749

Let's try dividing by 4:

168,735,749 ÷ 4 = 42,183,937.25

If the quotient is a whole number, then 4 and 42,183,937.25 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:

1 168,735,749
-1 168,735,749
Keep dividing by the next highest number until you cannot divide anymore.

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

1713915213,5593,6476,77324,91346,26747,411323,8691,854,23912,979,67324,105,107168,735,749
-1-7-13-91-521-3,559-3,647-6,773-24,913-46,267-47,411-323,869-1,854,239-12,979,673-24,105,107-168,735,749

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