Q: What are the factor combinations of the number 35,612,815?

 A:
Positive:   1 x 356128155 x 71225637 x 508754535 x 101750943 x 828205215 x 165641301 x 1183151505 x 23663
Negative: -1 x -35612815-5 x -7122563-7 x -5087545-35 x -1017509-43 x -828205-215 x -165641-301 x -118315-1505 x -23663


How do I find the factor combinations of the number 35,612,815?

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 35,612,815, 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 35,612,815
-1 -35,612,815

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 35,612,815.

Example:
1 x 35,612,815 = 35,612,815
and
-1 x -35,612,815 = 35,612,815
Notice both answers equal 35,612,815

With that explanation out of the way, let's continue. Next, we take the number 35,612,815 and divide it by 2:

35,612,815 ÷ 2 = 17,806,407.5

If the quotient is a whole number, then 2 and 17,806,407.5 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 35,612,815
-1 -35,612,815

Now, we try dividing 35,612,815 by 3:

35,612,815 ÷ 3 = 11,870,938.3333

If the quotient is a whole number, then 3 and 11,870,938.3333 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 35,612,815
-1 -35,612,815

Let's try dividing by 4:

35,612,815 ÷ 4 = 8,903,203.75

If the quotient is a whole number, then 4 and 8,903,203.75 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 35,612,815
-1 35,612,815
Keep dividing by the next highest number until you cannot divide anymore.

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

15735432153011,50523,663118,315165,641828,2051,017,5095,087,5457,122,56335,612,815
-1-5-7-35-43-215-301-1,505-23,663-118,315-165,641-828,205-1,017,509-5,087,545-7,122,563-35,612,815

More Examples

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