Q: What are the factor combinations of the number 40,130,405?

 A:
Positive:   1 x 401304055 x 80260817 x 573291535 x 11465831021 x 393051123 x 357355105 x 78615615 x 7147
Negative: -1 x -40130405-5 x -8026081-7 x -5732915-35 x -1146583-1021 x -39305-1123 x -35735-5105 x -7861-5615 x -7147


How do I find the factor combinations of the number 40,130,405?

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 40,130,405, 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 40,130,405
-1 -40,130,405

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 40,130,405.

Example:
1 x 40,130,405 = 40,130,405
and
-1 x -40,130,405 = 40,130,405
Notice both answers equal 40,130,405

With that explanation out of the way, let's continue. Next, we take the number 40,130,405 and divide it by 2:

40,130,405 ÷ 2 = 20,065,202.5

If the quotient is a whole number, then 2 and 20,065,202.5 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 40,130,405
-1 -40,130,405

Now, we try dividing 40,130,405 by 3:

40,130,405 ÷ 3 = 13,376,801.6667

If the quotient is a whole number, then 3 and 13,376,801.6667 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 40,130,405
-1 -40,130,405

Let's try dividing by 4:

40,130,405 ÷ 4 = 10,032,601.25

If the quotient is a whole number, then 4 and 10,032,601.25 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 40,130,405
-1 40,130,405
Keep dividing by the next highest number until you cannot divide anymore.

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

157351,0211,1235,1055,6157,1477,86135,73539,3051,146,5835,732,9158,026,08140,130,405
-1-5-7-35-1,021-1,123-5,105-5,615-7,147-7,861-35,735-39,305-1,146,583-5,732,915-8,026,081-40,130,405

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