Q: What are the factor combinations of the number 5,312,671?

 A:
Positive:   1 x 53126717 x 75895313 x 40866779 x 6724991 x 58381553 x 9607739 x 71891027 x 5173
Negative: -1 x -5312671-7 x -758953-13 x -408667-79 x -67249-91 x -58381-553 x -9607-739 x -7189-1027 x -5173


How do I find the factor combinations of the number 5,312,671?

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 5,312,671, 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 5,312,671
-1 -5,312,671

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 5,312,671.

Example:
1 x 5,312,671 = 5,312,671
and
-1 x -5,312,671 = 5,312,671
Notice both answers equal 5,312,671

With that explanation out of the way, let's continue. Next, we take the number 5,312,671 and divide it by 2:

5,312,671 ÷ 2 = 2,656,335.5

If the quotient is a whole number, then 2 and 2,656,335.5 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 5,312,671
-1 -5,312,671

Now, we try dividing 5,312,671 by 3:

5,312,671 ÷ 3 = 1,770,890.3333

If the quotient is a whole number, then 3 and 1,770,890.3333 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 5,312,671
-1 -5,312,671

Let's try dividing by 4:

5,312,671 ÷ 4 = 1,328,167.75

If the quotient is a whole number, then 4 and 1,328,167.75 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 5,312,671
-1 5,312,671
Keep dividing by the next highest number until you cannot divide anymore.

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

171379915537391,0275,1737,1899,60758,38167,249408,667758,9535,312,671
-1-7-13-79-91-553-739-1,027-5,173-7,189-9,607-58,381-67,249-408,667-758,953-5,312,671

More Examples

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