Q: What are the factor combinations of the number 402,515,501?

 A:
Positive:   1 x 40251550131 x 12984371157 x 2563793191 x 2107411433 x 9295974867 x 827035921 x 6798113423 x 29987
Negative: -1 x -402515501-31 x -12984371-157 x -2563793-191 x -2107411-433 x -929597-4867 x -82703-5921 x -67981-13423 x -29987


How do I find the factor combinations of the number 402,515,501?

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 402,515,501, 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.

1 402,515,501
-1 -402,515,501

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 402,515,501.

Example:
1 x 402,515,501 = 402,515,501
and
-1 x -402,515,501 = 402,515,501
Notice both answers equal 402,515,501

With that explanation out of the way, let's continue. Next, we take the number 402,515,501 and divide it by 2:

402,515,501 ÷ 2 = 201,257,750.5

If the quotient is a whole number, then 2 and 201,257,750.5 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:

1 402,515,501
-1 -402,515,501

Now, we try dividing 402,515,501 by 3:

402,515,501 ÷ 3 = 134,171,833.6667

If the quotient is a whole number, then 3 and 134,171,833.6667 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:

1 402,515,501
-1 -402,515,501

Let's try dividing by 4:

402,515,501 ÷ 4 = 100,628,875.25

If the quotient is a whole number, then 4 and 100,628,875.25 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:

1 402,515,501
-1 402,515,501
Keep dividing by the next highest number until you cannot divide anymore.

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

1311571914334,8675,92113,42329,98767,98182,703929,5972,107,4112,563,79312,984,371402,515,501
-1-31-157-191-433-4,867-5,921-13,423-29,987-67,981-82,703-929,597-2,107,411-2,563,793-12,984,371-402,515,501

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