Q: What are the factor combinations of the number 261,456,629?

 A:
Positive:   1 x 2614566297 x 3735094747 x 5562907329 x 794701653 x 4003931217 x 2148374571 x 571998519 x 30691
Negative: -1 x -261456629-7 x -37350947-47 x -5562907-329 x -794701-653 x -400393-1217 x -214837-4571 x -57199-8519 x -30691


How do I find the factor combinations of the number 261,456,629?

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 261,456,629, 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.

1 261,456,629
-1 -261,456,629

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 261,456,629.

Example:
1 x 261,456,629 = 261,456,629
and
-1 x -261,456,629 = 261,456,629
Notice both answers equal 261,456,629

With that explanation out of the way, let's continue. Next, we take the number 261,456,629 and divide it by 2:

261,456,629 ÷ 2 = 130,728,314.5

If the quotient is a whole number, then 2 and 130,728,314.5 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:

1 261,456,629
-1 -261,456,629

Now, we try dividing 261,456,629 by 3:

261,456,629 ÷ 3 = 87,152,209.6667

If the quotient is a whole number, then 3 and 87,152,209.6667 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:

1 261,456,629
-1 -261,456,629

Let's try dividing by 4:

261,456,629 ÷ 4 = 65,364,157.25

If the quotient is a whole number, then 4 and 65,364,157.25 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:

1 261,456,629
-1 261,456,629
Keep dividing by the next highest number until you cannot divide anymore.

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

17473296531,2174,5718,51930,69157,199214,837400,393794,7015,562,90737,350,947261,456,629
-1-7-47-329-653-1,217-4,571-8,519-30,691-57,199-214,837-400,393-794,701-5,562,907-37,350,947-261,456,629

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