Q: What are the factor combinations of the number 877,164?

 A:
Positive:   1 x 8771642 x 4385823 x 2923884 x 2192916 x 14619412 x 7309767 x 13092134 x 6546201 x 4364268 x 3273402 x 2182804 x 1091
Negative: -1 x -877164-2 x -438582-3 x -292388-4 x -219291-6 x -146194-12 x -73097-67 x -13092-134 x -6546-201 x -4364-268 x -3273-402 x -2182-804 x -1091


How do I find the factor combinations of the number 877,164?

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 877,164, 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.

1 877,164
-1 -877,164

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 877,164.

Example:
1 x 877,164 = 877,164
and
-1 x -877,164 = 877,164
Notice both answers equal 877,164

With that explanation out of the way, let's continue. Next, we take the number 877,164 and divide it by 2:

877,164 ÷ 2 = 438,582

If the quotient is a whole number, then 2 and 438,582 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 438,582 877,164
-1 -2 -438,582 -877,164

Now, we try dividing 877,164 by 3:

877,164 ÷ 3 = 292,388

If the quotient is a whole number, then 3 and 292,388 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 292,388 438,582 877,164
-1 -2 -3 -292,388 -438,582 -877,164

Let's try dividing by 4:

877,164 ÷ 4 = 219,291

If the quotient is a whole number, then 4 and 219,291 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 219,291 292,388 438,582 877,164
-1 -2 -3 -4 -219,291 -292,388 -438,582 877,164
Keep dividing by the next highest number until you cannot divide anymore.

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

1234612671342012684028041,0912,1823,2734,3646,54613,09273,097146,194219,291292,388438,582877,164
-1-2-3-4-6-12-67-134-201-268-402-804-1,091-2,182-3,273-4,364-6,546-13,092-73,097-146,194-219,291-292,388-438,582-877,164

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