Q: What are the factor combinations of the number 405,730,007?

 A:
Positive:   1 x 40573000717 x 23866471167 x 2429521241 x 1683527593 x 6841992839 x 1429134097 x 9903110081 x 40247
Negative: -1 x -405730007-17 x -23866471-167 x -2429521-241 x -1683527-593 x -684199-2839 x -142913-4097 x -99031-10081 x -40247


How do I find the factor combinations of the number 405,730,007?

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 405,730,007, 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.

1 405,730,007
-1 -405,730,007

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 405,730,007.

Example:
1 x 405,730,007 = 405,730,007
and
-1 x -405,730,007 = 405,730,007
Notice both answers equal 405,730,007

With that explanation out of the way, let's continue. Next, we take the number 405,730,007 and divide it by 2:

405,730,007 ÷ 2 = 202,865,003.5

If the quotient is a whole number, then 2 and 202,865,003.5 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:

1 405,730,007
-1 -405,730,007

Now, we try dividing 405,730,007 by 3:

405,730,007 ÷ 3 = 135,243,335.6667

If the quotient is a whole number, then 3 and 135,243,335.6667 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:

1 405,730,007
-1 -405,730,007

Let's try dividing by 4:

405,730,007 ÷ 4 = 101,432,501.75

If the quotient is a whole number, then 4 and 101,432,501.75 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:

1 405,730,007
-1 405,730,007
Keep dividing by the next highest number until you cannot divide anymore.

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

1171672415932,8394,09710,08140,24799,031142,913684,1991,683,5272,429,52123,866,471405,730,007
-1-17-167-241-593-2,839-4,097-10,081-40,247-99,031-142,913-684,199-1,683,527-2,429,521-23,866,471-405,730,007

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