Q: What are the factor combinations of the number 401,560?

 A:
Positive:   1 x 4015602 x 2007804 x 1003905 x 803128 x 5019510 x 4015620 x 2007840 x 10039
Negative: -1 x -401560-2 x -200780-4 x -100390-5 x -80312-8 x -50195-10 x -40156-20 x -20078-40 x -10039


How do I find the factor combinations of the number 401,560?

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 401,560, 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.

1 401,560
-1 -401,560

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 401,560.

Example:
1 x 401,560 = 401,560
and
-1 x -401,560 = 401,560
Notice both answers equal 401,560

With that explanation out of the way, let's continue. Next, we take the number 401,560 and divide it by 2:

401,560 ÷ 2 = 200,780

If the quotient is a whole number, then 2 and 200,780 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 200,780 401,560
-1 -2 -200,780 -401,560

Now, we try dividing 401,560 by 3:

401,560 ÷ 3 = 133,853.3333

If the quotient is a whole number, then 3 and 133,853.3333 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 2 200,780 401,560
-1 -2 -200,780 -401,560

Let's try dividing by 4:

401,560 ÷ 4 = 100,390

If the quotient is a whole number, then 4 and 100,390 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 100,390 200,780 401,560
-1 -2 -4 -100,390 -200,780 401,560
Keep dividing by the next highest number until you cannot divide anymore.

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

1245810204010,03920,07840,15650,19580,312100,390200,780401,560
-1-2-4-5-8-10-20-40-10,039-20,078-40,156-50,195-80,312-100,390-200,780-401,560

More Examples

Here are some more numbers to try:

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