Q: What are the factor combinations of the number 402,134,305?

 A:
Positive:   1 x 4021343055 x 80426861157 x 2561365229 x 1756045785 x 5122731145 x 3512092237 x 17976511185 x 35953
Negative: -1 x -402134305-5 x -80426861-157 x -2561365-229 x -1756045-785 x -512273-1145 x -351209-2237 x -179765-11185 x -35953


How do I find the factor combinations of the number 402,134,305?

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 402,134,305, 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.

1 402,134,305
-1 -402,134,305

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 402,134,305.

Example:
1 x 402,134,305 = 402,134,305
and
-1 x -402,134,305 = 402,134,305
Notice both answers equal 402,134,305

With that explanation out of the way, let's continue. Next, we take the number 402,134,305 and divide it by 2:

402,134,305 ÷ 2 = 201,067,152.5

If the quotient is a whole number, then 2 and 201,067,152.5 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:

1 402,134,305
-1 -402,134,305

Now, we try dividing 402,134,305 by 3:

402,134,305 ÷ 3 = 134,044,768.3333

If the quotient is a whole number, then 3 and 134,044,768.3333 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:

1 402,134,305
-1 -402,134,305

Let's try dividing by 4:

402,134,305 ÷ 4 = 100,533,576.25

If the quotient is a whole number, then 4 and 100,533,576.25 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:

1 402,134,305
-1 402,134,305
Keep dividing by the next highest number until you cannot divide anymore.

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

151572297851,1452,23711,18535,953179,765351,209512,2731,756,0452,561,36580,426,861402,134,305
-1-5-157-229-785-1,145-2,237-11,185-35,953-179,765-351,209-512,273-1,756,045-2,561,365-80,426,861-402,134,305

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