Q: What are the factor combinations of the number 400,061?

 A:
Positive:   1 x 40006117 x 23533101 x 3961233 x 1717
Negative: -1 x -400061-17 x -23533-101 x -3961-233 x -1717


How do I find the factor combinations of the number 400,061?

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 400,061, 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.

1 400,061
-1 -400,061

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 400,061.

Example:
1 x 400,061 = 400,061
and
-1 x -400,061 = 400,061
Notice both answers equal 400,061

With that explanation out of the way, let's continue. Next, we take the number 400,061 and divide it by 2:

400,061 ÷ 2 = 200,030.5

If the quotient is a whole number, then 2 and 200,030.5 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:

1 400,061
-1 -400,061

Now, we try dividing 400,061 by 3:

400,061 ÷ 3 = 133,353.6667

If the quotient is a whole number, then 3 and 133,353.6667 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:

1 400,061
-1 -400,061

Let's try dividing by 4:

400,061 ÷ 4 = 100,015.25

If the quotient is a whole number, then 4 and 100,015.25 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:

1 400,061
-1 400,061
Keep dividing by the next highest number until you cannot divide anymore.

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

1171012331,7173,96123,533400,061
-1-17-101-233-1,717-3,961-23,533-400,061

More Examples

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