Q: What are the factor combinations of the number 125,346,221?

 A:
Positive:   1 x 1253462217 x 1790660311 x 1139511113 x 964201777 x 162787391 x 1377431143 x 8765471001 x 125221
Negative: -1 x -125346221-7 x -17906603-11 x -11395111-13 x -9642017-77 x -1627873-91 x -1377431-143 x -876547-1001 x -125221


How do I find the factor combinations of the number 125,346,221?

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 125,346,221, 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.

1 125,346,221
-1 -125,346,221

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 125,346,221.

Example:
1 x 125,346,221 = 125,346,221
and
-1 x -125,346,221 = 125,346,221
Notice both answers equal 125,346,221

With that explanation out of the way, let's continue. Next, we take the number 125,346,221 and divide it by 2:

125,346,221 ÷ 2 = 62,673,110.5

If the quotient is a whole number, then 2 and 62,673,110.5 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:

1 125,346,221
-1 -125,346,221

Now, we try dividing 125,346,221 by 3:

125,346,221 ÷ 3 = 41,782,073.6667

If the quotient is a whole number, then 3 and 41,782,073.6667 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:

1 125,346,221
-1 -125,346,221

Let's try dividing by 4:

125,346,221 ÷ 4 = 31,336,555.25

If the quotient is a whole number, then 4 and 31,336,555.25 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:

1 125,346,221
-1 125,346,221
Keep dividing by the next highest number until you cannot divide anymore.

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

17111377911431,001125,221876,5471,377,4311,627,8739,642,01711,395,11117,906,603125,346,221
-1-7-11-13-77-91-143-1,001-125,221-876,547-1,377,431-1,627,873-9,642,017-11,395,111-17,906,603-125,346,221

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