Q: What are the factor combinations of the number 351,144,661?

 A:
Positive:   1 x 3511446617 x 5016352347 x 7471163329 x 1067309877 x 4003931217 x 2885336139 x 571998519 x 41219
Negative: -1 x -351144661-7 x -50163523-47 x -7471163-329 x -1067309-877 x -400393-1217 x -288533-6139 x -57199-8519 x -41219


How do I find the factor combinations of the number 351,144,661?

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 351,144,661, 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.

1 351,144,661
-1 -351,144,661

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 351,144,661.

Example:
1 x 351,144,661 = 351,144,661
and
-1 x -351,144,661 = 351,144,661
Notice both answers equal 351,144,661

With that explanation out of the way, let's continue. Next, we take the number 351,144,661 and divide it by 2:

351,144,661 ÷ 2 = 175,572,330.5

If the quotient is a whole number, then 2 and 175,572,330.5 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:

1 351,144,661
-1 -351,144,661

Now, we try dividing 351,144,661 by 3:

351,144,661 ÷ 3 = 117,048,220.3333

If the quotient is a whole number, then 3 and 117,048,220.3333 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:

1 351,144,661
-1 -351,144,661

Let's try dividing by 4:

351,144,661 ÷ 4 = 87,786,165.25

If the quotient is a whole number, then 4 and 87,786,165.25 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:

1 351,144,661
-1 351,144,661
Keep dividing by the next highest number until you cannot divide anymore.

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

17473298771,2176,1398,51941,21957,199288,533400,3931,067,3097,471,16350,163,523351,144,661
-1-7-47-329-877-1,217-6,139-8,519-41,219-57,199-288,533-400,393-1,067,309-7,471,163-50,163,523-351,144,661

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