Q: What are the factor combinations of the number 7,698,971?

 A:
Positive:   1 x 76989717 x 109985319 x 405209107 x 71953133 x 57887541 x 14231749 x 102792033 x 3787
Negative: -1 x -7698971-7 x -1099853-19 x -405209-107 x -71953-133 x -57887-541 x -14231-749 x -10279-2033 x -3787


How do I find the factor combinations of the number 7,698,971?

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 7,698,971, 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 7,698,971
-1 -7,698,971

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 7,698,971.

Example:
1 x 7,698,971 = 7,698,971
and
-1 x -7,698,971 = 7,698,971
Notice both answers equal 7,698,971

With that explanation out of the way, let's continue. Next, we take the number 7,698,971 and divide it by 2:

7,698,971 ÷ 2 = 3,849,485.5

If the quotient is a whole number, then 2 and 3,849,485.5 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 7,698,971
-1 -7,698,971

Now, we try dividing 7,698,971 by 3:

7,698,971 ÷ 3 = 2,566,323.6667

If the quotient is a whole number, then 3 and 2,566,323.6667 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 7,698,971
-1 -7,698,971

Let's try dividing by 4:

7,698,971 ÷ 4 = 1,924,742.75

If the quotient is a whole number, then 4 and 1,924,742.75 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 7,698,971
-1 7,698,971
Keep dividing by the next highest number until you cannot divide anymore.

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

17191071335417492,0333,78710,27914,23157,88771,953405,2091,099,8537,698,971
-1-7-19-107-133-541-749-2,033-3,787-10,279-14,231-57,887-71,953-405,209-1,099,853-7,698,971

More Examples

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