Q: What are the factor combinations of the number 211,131,007?

 A:
Positive:   1 x 21113100717 x 1241947123 x 9179609197 x 1071731391 x 5399772741 x 770273349 x 630434531 x 46597
Negative: -1 x -211131007-17 x -12419471-23 x -9179609-197 x -1071731-391 x -539977-2741 x -77027-3349 x -63043-4531 x -46597


How do I find the factor combinations of the number 211,131,007?

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 211,131,007, 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.

1 211,131,007
-1 -211,131,007

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 211,131,007.

Example:
1 x 211,131,007 = 211,131,007
and
-1 x -211,131,007 = 211,131,007
Notice both answers equal 211,131,007

With that explanation out of the way, let's continue. Next, we take the number 211,131,007 and divide it by 2:

211,131,007 ÷ 2 = 105,565,503.5

If the quotient is a whole number, then 2 and 105,565,503.5 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:

1 211,131,007
-1 -211,131,007

Now, we try dividing 211,131,007 by 3:

211,131,007 ÷ 3 = 70,377,002.3333

If the quotient is a whole number, then 3 and 70,377,002.3333 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:

1 211,131,007
-1 -211,131,007

Let's try dividing by 4:

211,131,007 ÷ 4 = 52,782,751.75

If the quotient is a whole number, then 4 and 52,782,751.75 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:

1 211,131,007
-1 211,131,007
Keep dividing by the next highest number until you cannot divide anymore.

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

117231973912,7413,3494,53146,59763,04377,027539,9771,071,7319,179,60912,419,471211,131,007
-1-17-23-197-391-2,741-3,349-4,531-46,597-63,043-77,027-539,977-1,071,731-9,179,609-12,419,471-211,131,007

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