Q: What are the factor combinations of the number 35,400,715?

 A:
Positive:   1 x 354007155 x 70801437 x 505724517 x 208239535 x 101144985 x 416479119 x 297485595 x 59497
Negative: -1 x -35400715-5 x -7080143-7 x -5057245-17 x -2082395-35 x -1011449-85 x -416479-119 x -297485-595 x -59497


How do I find the factor combinations of the number 35,400,715?

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 35,400,715, 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 35,400,715
-1 -35,400,715

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 35,400,715.

Example:
1 x 35,400,715 = 35,400,715
and
-1 x -35,400,715 = 35,400,715
Notice both answers equal 35,400,715

With that explanation out of the way, let's continue. Next, we take the number 35,400,715 and divide it by 2:

35,400,715 ÷ 2 = 17,700,357.5

If the quotient is a whole number, then 2 and 17,700,357.5 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 35,400,715
-1 -35,400,715

Now, we try dividing 35,400,715 by 3:

35,400,715 ÷ 3 = 11,800,238.3333

If the quotient is a whole number, then 3 and 11,800,238.3333 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 35,400,715
-1 -35,400,715

Let's try dividing by 4:

35,400,715 ÷ 4 = 8,850,178.75

If the quotient is a whole number, then 4 and 8,850,178.75 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 35,400,715
-1 35,400,715
Keep dividing by the next highest number until you cannot divide anymore.

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

15717358511959559,497297,485416,4791,011,4492,082,3955,057,2457,080,14335,400,715
-1-5-7-17-35-85-119-595-59,497-297,485-416,479-1,011,449-2,082,395-5,057,245-7,080,143-35,400,715

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