Q: What are the factor combinations of the number 3,629,449?

 A:
Positive:   1 x 362944917 x 21349731 x 11707971 x 5111997 x 37417527 x 68871207 x 30071649 x 2201
Negative: -1 x -3629449-17 x -213497-31 x -117079-71 x -51119-97 x -37417-527 x -6887-1207 x -3007-1649 x -2201


How do I find the factor combinations of the number 3,629,449?

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 3,629,449, 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 3,629,449
-1 -3,629,449

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 3,629,449.

Example:
1 x 3,629,449 = 3,629,449
and
-1 x -3,629,449 = 3,629,449
Notice both answers equal 3,629,449

With that explanation out of the way, let's continue. Next, we take the number 3,629,449 and divide it by 2:

3,629,449 ÷ 2 = 1,814,724.5

If the quotient is a whole number, then 2 and 1,814,724.5 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 3,629,449
-1 -3,629,449

Now, we try dividing 3,629,449 by 3:

3,629,449 ÷ 3 = 1,209,816.3333

If the quotient is a whole number, then 3 and 1,209,816.3333 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 3,629,449
-1 -3,629,449

Let's try dividing by 4:

3,629,449 ÷ 4 = 907,362.25

If the quotient is a whole number, then 4 and 907,362.25 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 3,629,449
-1 3,629,449
Keep dividing by the next highest number until you cannot divide anymore.

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

1173171975271,2071,6492,2013,0076,88737,41751,119117,079213,4973,629,449
-1-17-31-71-97-527-1,207-1,649-2,201-3,007-6,887-37,417-51,119-117,079-213,497-3,629,449

More Examples

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