Q: What are the factor combinations of the number 210,042,413?

 A:
Positive:   1 x 2100424137 x 30006059167 x 1257739353 x 595021509 x 4126571169 x 1796772471 x 850033563 x 58951
Negative: -1 x -210042413-7 x -30006059-167 x -1257739-353 x -595021-509 x -412657-1169 x -179677-2471 x -85003-3563 x -58951


How do I find the factor combinations of the number 210,042,413?

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 210,042,413, 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.

1 210,042,413
-1 -210,042,413

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 210,042,413.

Example:
1 x 210,042,413 = 210,042,413
and
-1 x -210,042,413 = 210,042,413
Notice both answers equal 210,042,413

With that explanation out of the way, let's continue. Next, we take the number 210,042,413 and divide it by 2:

210,042,413 ÷ 2 = 105,021,206.5

If the quotient is a whole number, then 2 and 105,021,206.5 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:

1 210,042,413
-1 -210,042,413

Now, we try dividing 210,042,413 by 3:

210,042,413 ÷ 3 = 70,014,137.6667

If the quotient is a whole number, then 3 and 70,014,137.6667 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:

1 210,042,413
-1 -210,042,413

Let's try dividing by 4:

210,042,413 ÷ 4 = 52,510,603.25

If the quotient is a whole number, then 4 and 52,510,603.25 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:

1 210,042,413
-1 210,042,413
Keep dividing by the next highest number until you cannot divide anymore.

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

171673535091,1692,4713,56358,95185,003179,677412,657595,0211,257,73930,006,059210,042,413
-1-7-167-353-509-1,169-2,471-3,563-58,951-85,003-179,677-412,657-595,021-1,257,739-30,006,059-210,042,413

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