Q: What are the factor combinations of the number 354,320,743?

 A:
Positive:   1 x 3543207437 x 5061724971 x 4990433497 x 712919613 x 5780111163 x 3046614291 x 825738141 x 43523
Negative: -1 x -354320743-7 x -50617249-71 x -4990433-497 x -712919-613 x -578011-1163 x -304661-4291 x -82573-8141 x -43523


How do I find the factor combinations of the number 354,320,743?

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 354,320,743, 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.

1 354,320,743
-1 -354,320,743

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 354,320,743.

Example:
1 x 354,320,743 = 354,320,743
and
-1 x -354,320,743 = 354,320,743
Notice both answers equal 354,320,743

With that explanation out of the way, let's continue. Next, we take the number 354,320,743 and divide it by 2:

354,320,743 ÷ 2 = 177,160,371.5

If the quotient is a whole number, then 2 and 177,160,371.5 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:

1 354,320,743
-1 -354,320,743

Now, we try dividing 354,320,743 by 3:

354,320,743 ÷ 3 = 118,106,914.3333

If the quotient is a whole number, then 3 and 118,106,914.3333 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:

1 354,320,743
-1 -354,320,743

Let's try dividing by 4:

354,320,743 ÷ 4 = 88,580,185.75

If the quotient is a whole number, then 4 and 88,580,185.75 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:

1 354,320,743
-1 354,320,743
Keep dividing by the next highest number until you cannot divide anymore.

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

17714976131,1634,2918,14143,52382,573304,661578,011712,9194,990,43350,617,249354,320,743
-1-7-71-497-613-1,163-4,291-8,141-43,523-82,573-304,661-578,011-712,919-4,990,433-50,617,249-354,320,743

More Examples

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