Q: What are the factor combinations of the number 402,535?

 A:
Positive:   1 x 4025355 x 805077 x 5750531 x 1298535 x 1150149 x 821553 x 7595155 x 2597217 x 1855245 x 1643265 x 1519371 x 1085
Negative: -1 x -402535-5 x -80507-7 x -57505-31 x -12985-35 x -11501-49 x -8215-53 x -7595-155 x -2597-217 x -1855-245 x -1643-265 x -1519-371 x -1085


How do I find the factor combinations of the number 402,535?

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 402,535, 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.

1 402,535
-1 -402,535

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 402,535.

Example:
1 x 402,535 = 402,535
and
-1 x -402,535 = 402,535
Notice both answers equal 402,535

With that explanation out of the way, let's continue. Next, we take the number 402,535 and divide it by 2:

402,535 ÷ 2 = 201,267.5

If the quotient is a whole number, then 2 and 201,267.5 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:

1 402,535
-1 -402,535

Now, we try dividing 402,535 by 3:

402,535 ÷ 3 = 134,178.3333

If the quotient is a whole number, then 3 and 134,178.3333 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:

1 402,535
-1 -402,535

Let's try dividing by 4:

402,535 ÷ 4 = 100,633.75

If the quotient is a whole number, then 4 and 100,633.75 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:

1 402,535
-1 402,535
Keep dividing by the next highest number until you cannot divide anymore.

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

157313549531552172452653711,0851,5191,6431,8552,5977,5958,21511,50112,98557,50580,507402,535
-1-5-7-31-35-49-53-155-217-245-265-371-1,085-1,519-1,643-1,855-2,597-7,595-8,215-11,501-12,985-57,505-80,507-402,535

More Examples

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