Q: What are the factor combinations of the number 4,610,749?

 A:
Positive:   1 x 461074911 x 41915913 x 35467319 x 242671143 x 32243209 x 22061247 x 186671697 x 2717
Negative: -1 x -4610749-11 x -419159-13 x -354673-19 x -242671-143 x -32243-209 x -22061-247 x -18667-1697 x -2717


How do I find the factor combinations of the number 4,610,749?

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 4,610,749, 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 4,610,749
-1 -4,610,749

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 4,610,749.

Example:
1 x 4,610,749 = 4,610,749
and
-1 x -4,610,749 = 4,610,749
Notice both answers equal 4,610,749

With that explanation out of the way, let's continue. Next, we take the number 4,610,749 and divide it by 2:

4,610,749 ÷ 2 = 2,305,374.5

If the quotient is a whole number, then 2 and 2,305,374.5 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 4,610,749
-1 -4,610,749

Now, we try dividing 4,610,749 by 3:

4,610,749 ÷ 3 = 1,536,916.3333

If the quotient is a whole number, then 3 and 1,536,916.3333 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 4,610,749
-1 -4,610,749

Let's try dividing by 4:

4,610,749 ÷ 4 = 1,152,687.25

If the quotient is a whole number, then 4 and 1,152,687.25 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 4,610,749
-1 4,610,749
Keep dividing by the next highest number until you cannot divide anymore.

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

11113191432092471,6972,71718,66722,06132,243242,671354,673419,1594,610,749
-1-11-13-19-143-209-247-1,697-2,717-18,667-22,061-32,243-242,671-354,673-419,159-4,610,749

More Examples

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