Q: What are the factor combinations of the number 40,694,465?

 A:
Positive:   1 x 406944655 x 81388937 x 581349535 x 1162699661 x 615651759 x 231353305 x 123134627 x 8795
Negative: -1 x -40694465-5 x -8138893-7 x -5813495-35 x -1162699-661 x -61565-1759 x -23135-3305 x -12313-4627 x -8795


How do I find the factor combinations of the number 40,694,465?

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 40,694,465, 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 40,694,465
-1 -40,694,465

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 40,694,465.

Example:
1 x 40,694,465 = 40,694,465
and
-1 x -40,694,465 = 40,694,465
Notice both answers equal 40,694,465

With that explanation out of the way, let's continue. Next, we take the number 40,694,465 and divide it by 2:

40,694,465 ÷ 2 = 20,347,232.5

If the quotient is a whole number, then 2 and 20,347,232.5 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 40,694,465
-1 -40,694,465

Now, we try dividing 40,694,465 by 3:

40,694,465 ÷ 3 = 13,564,821.6667

If the quotient is a whole number, then 3 and 13,564,821.6667 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 40,694,465
-1 -40,694,465

Let's try dividing by 4:

40,694,465 ÷ 4 = 10,173,616.25

If the quotient is a whole number, then 4 and 10,173,616.25 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 40,694,465
-1 40,694,465
Keep dividing by the next highest number until you cannot divide anymore.

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

157356611,7593,3054,6278,79512,31323,13561,5651,162,6995,813,4958,138,89340,694,465
-1-5-7-35-661-1,759-3,305-4,627-8,795-12,313-23,135-61,565-1,162,699-5,813,495-8,138,893-40,694,465

More Examples

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