Q: What are the factor combinations of the number 401,635?

 A:
Positive:   1 x 4016355 x 8032713 x 3089537 x 1085565 x 6179167 x 2405185 x 2171481 x 835
Negative: -1 x -401635-5 x -80327-13 x -30895-37 x -10855-65 x -6179-167 x -2405-185 x -2171-481 x -835


How do I find the factor combinations of the number 401,635?

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 401,635, 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.

1 401,635
-1 -401,635

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 401,635.

Example:
1 x 401,635 = 401,635
and
-1 x -401,635 = 401,635
Notice both answers equal 401,635

With that explanation out of the way, let's continue. Next, we take the number 401,635 and divide it by 2:

401,635 ÷ 2 = 200,817.5

If the quotient is a whole number, then 2 and 200,817.5 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:

1 401,635
-1 -401,635

Now, we try dividing 401,635 by 3:

401,635 ÷ 3 = 133,878.3333

If the quotient is a whole number, then 3 and 133,878.3333 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:

1 401,635
-1 -401,635

Let's try dividing by 4:

401,635 ÷ 4 = 100,408.75

If the quotient is a whole number, then 4 and 100,408.75 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:

1 401,635
-1 401,635
Keep dividing by the next highest number until you cannot divide anymore.

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

151337651671854818352,1712,4056,17910,85530,89580,327401,635
-1-5-13-37-65-167-185-481-835-2,171-2,405-6,179-10,855-30,895-80,327-401,635

More Examples

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