Q: What are the factor combinations of the number 106,104,607?

 A:
Positive:   1 x 1061046077 x 1515780119 x 558445343 x 2467549133 x 797779301 x 352507817 x 1298715719 x 18553
Negative: -1 x -106104607-7 x -15157801-19 x -5584453-43 x -2467549-133 x -797779-301 x -352507-817 x -129871-5719 x -18553


How do I find the factor combinations of the number 106,104,607?

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 106,104,607, 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.

1 106,104,607
-1 -106,104,607

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 106,104,607.

Example:
1 x 106,104,607 = 106,104,607
and
-1 x -106,104,607 = 106,104,607
Notice both answers equal 106,104,607

With that explanation out of the way, let's continue. Next, we take the number 106,104,607 and divide it by 2:

106,104,607 ÷ 2 = 53,052,303.5

If the quotient is a whole number, then 2 and 53,052,303.5 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:

1 106,104,607
-1 -106,104,607

Now, we try dividing 106,104,607 by 3:

106,104,607 ÷ 3 = 35,368,202.3333

If the quotient is a whole number, then 3 and 35,368,202.3333 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:

1 106,104,607
-1 -106,104,607

Let's try dividing by 4:

106,104,607 ÷ 4 = 26,526,151.75

If the quotient is a whole number, then 4 and 26,526,151.75 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:

1 106,104,607
-1 106,104,607
Keep dividing by the next highest number until you cannot divide anymore.

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

1719431333018175,71918,553129,871352,507797,7792,467,5495,584,45315,157,801106,104,607
-1-7-19-43-133-301-817-5,719-18,553-129,871-352,507-797,779-2,467,549-5,584,453-15,157,801-106,104,607

More Examples

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