Q: What are the factor combinations of the number 721,146,415?

 A:
Positive:   1 x 7211464155 x 14422928311 x 6555876555 x 131117531499 x 4810857495 x 962178747 x 8244516489 x 43735
Negative: -1 x -721146415-5 x -144229283-11 x -65558765-55 x -13111753-1499 x -481085-7495 x -96217-8747 x -82445-16489 x -43735


How do I find the factor combinations of the number 721,146,415?

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 721,146,415, 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.

1 721,146,415
-1 -721,146,415

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 721,146,415.

Example:
1 x 721,146,415 = 721,146,415
and
-1 x -721,146,415 = 721,146,415
Notice both answers equal 721,146,415

With that explanation out of the way, let's continue. Next, we take the number 721,146,415 and divide it by 2:

721,146,415 ÷ 2 = 360,573,207.5

If the quotient is a whole number, then 2 and 360,573,207.5 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:

1 721,146,415
-1 -721,146,415

Now, we try dividing 721,146,415 by 3:

721,146,415 ÷ 3 = 240,382,138.3333

If the quotient is a whole number, then 3 and 240,382,138.3333 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:

1 721,146,415
-1 -721,146,415

Let's try dividing by 4:

721,146,415 ÷ 4 = 180,286,603.75

If the quotient is a whole number, then 4 and 180,286,603.75 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:

1 721,146,415
-1 721,146,415
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551,4997,4958,74716,48943,73582,44596,217481,08513,111,75365,558,765144,229,283721,146,415
-1-5-11-55-1,499-7,495-8,747-16,489-43,735-82,445-96,217-481,085-13,111,753-65,558,765-144,229,283-721,146,415

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