Q: What are the factor combinations of the number 350,145,689?

 A:
Positive:   1 x 35014568937 x 946339743 x 8142923101 x 34667891591 x 2200792179 x 1606913737 x 936974343 x 80623
Negative: -1 x -350145689-37 x -9463397-43 x -8142923-101 x -3466789-1591 x -220079-2179 x -160691-3737 x -93697-4343 x -80623


How do I find the factor combinations of the number 350,145,689?

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 350,145,689, 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.

1 350,145,689
-1 -350,145,689

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 350,145,689.

Example:
1 x 350,145,689 = 350,145,689
and
-1 x -350,145,689 = 350,145,689
Notice both answers equal 350,145,689

With that explanation out of the way, let's continue. Next, we take the number 350,145,689 and divide it by 2:

350,145,689 ÷ 2 = 175,072,844.5

If the quotient is a whole number, then 2 and 175,072,844.5 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:

1 350,145,689
-1 -350,145,689

Now, we try dividing 350,145,689 by 3:

350,145,689 ÷ 3 = 116,715,229.6667

If the quotient is a whole number, then 3 and 116,715,229.6667 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:

1 350,145,689
-1 -350,145,689

Let's try dividing by 4:

350,145,689 ÷ 4 = 87,536,422.25

If the quotient is a whole number, then 4 and 87,536,422.25 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:

1 350,145,689
-1 350,145,689
Keep dividing by the next highest number until you cannot divide anymore.

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

137431011,5912,1793,7374,34380,62393,697160,691220,0793,466,7898,142,9239,463,397350,145,689
-1-37-43-101-1,591-2,179-3,737-4,343-80,623-93,697-160,691-220,079-3,466,789-8,142,923-9,463,397-350,145,689

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