Q: What are the factor combinations of the number 654,365,046?

 A:
Positive:   1 x 6543650462 x 3271825233 x 2181216826 x 109060841443 x 1477122886 x 7385611329 x 4923742658 x 246187
Negative: -1 x -654365046-2 x -327182523-3 x -218121682-6 x -109060841-443 x -1477122-886 x -738561-1329 x -492374-2658 x -246187


How do I find the factor combinations of the number 654,365,046?

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 654,365,046, 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.

1 654,365,046
-1 -654,365,046

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 654,365,046.

Example:
1 x 654,365,046 = 654,365,046
and
-1 x -654,365,046 = 654,365,046
Notice both answers equal 654,365,046

With that explanation out of the way, let's continue. Next, we take the number 654,365,046 and divide it by 2:

654,365,046 ÷ 2 = 327,182,523

If the quotient is a whole number, then 2 and 327,182,523 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 327,182,523 654,365,046
-1 -2 -327,182,523 -654,365,046

Now, we try dividing 654,365,046 by 3:

654,365,046 ÷ 3 = 218,121,682

If the quotient is a whole number, then 3 and 218,121,682 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 218,121,682 327,182,523 654,365,046
-1 -2 -3 -218,121,682 -327,182,523 -654,365,046

Let's try dividing by 4:

654,365,046 ÷ 4 = 163,591,261.5

If the quotient is a whole number, then 4 and 163,591,261.5 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 2 3 218,121,682 327,182,523 654,365,046
-1 -2 -3 -218,121,682 -327,182,523 654,365,046
Keep dividing by the next highest number until you cannot divide anymore.

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

12364438861,3292,658246,187492,374738,5611,477,122109,060,841218,121,682327,182,523654,365,046
-1-2-3-6-443-886-1,329-2,658-246,187-492,374-738,561-1,477,122-109,060,841-218,121,682-327,182,523-654,365,046

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