Q: What are the factor combinations of the number 353,421,523?

 A:
Positive:   1 x 3534215237 x 5048878913 x 2718627191 x 3883753101 x 3499223707 x 4998891313 x 2691719191 x 38453
Negative: -1 x -353421523-7 x -50488789-13 x -27186271-91 x -3883753-101 x -3499223-707 x -499889-1313 x -269171-9191 x -38453


How do I find the factor combinations of the number 353,421,523?

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 353,421,523, 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.

1 353,421,523
-1 -353,421,523

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 353,421,523.

Example:
1 x 353,421,523 = 353,421,523
and
-1 x -353,421,523 = 353,421,523
Notice both answers equal 353,421,523

With that explanation out of the way, let's continue. Next, we take the number 353,421,523 and divide it by 2:

353,421,523 ÷ 2 = 176,710,761.5

If the quotient is a whole number, then 2 and 176,710,761.5 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:

1 353,421,523
-1 -353,421,523

Now, we try dividing 353,421,523 by 3:

353,421,523 ÷ 3 = 117,807,174.3333

If the quotient is a whole number, then 3 and 117,807,174.3333 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:

1 353,421,523
-1 -353,421,523

Let's try dividing by 4:

353,421,523 ÷ 4 = 88,355,380.75

If the quotient is a whole number, then 4 and 88,355,380.75 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:

1 353,421,523
-1 353,421,523
Keep dividing by the next highest number until you cannot divide anymore.

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

1713911017071,3139,19138,453269,171499,8893,499,2233,883,75327,186,27150,488,789353,421,523
-1-7-13-91-101-707-1,313-9,191-38,453-269,171-499,889-3,499,223-3,883,753-27,186,271-50,488,789-353,421,523

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