Q: What are the factor combinations of the number 601,864?

 A:
Positive:   1 x 6018642 x 3009324 x 1504668 x 7523323 x 2616846 x 1308492 x 6542184 x 3271
Negative: -1 x -601864-2 x -300932-4 x -150466-8 x -75233-23 x -26168-46 x -13084-92 x -6542-184 x -3271


How do I find the factor combinations of the number 601,864?

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 601,864, 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.

1 601,864
-1 -601,864

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 601,864.

Example:
1 x 601,864 = 601,864
and
-1 x -601,864 = 601,864
Notice both answers equal 601,864

With that explanation out of the way, let's continue. Next, we take the number 601,864 and divide it by 2:

601,864 ÷ 2 = 300,932

If the quotient is a whole number, then 2 and 300,932 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 2 300,932 601,864
-1 -2 -300,932 -601,864

Now, we try dividing 601,864 by 3:

601,864 ÷ 3 = 200,621.3333

If the quotient is a whole number, then 3 and 200,621.3333 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 2 300,932 601,864
-1 -2 -300,932 -601,864

Let's try dividing by 4:

601,864 ÷ 4 = 150,466

If the quotient is a whole number, then 4 and 150,466 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 4 150,466 300,932 601,864
-1 -2 -4 -150,466 -300,932 601,864
Keep dividing by the next highest number until you cannot divide anymore.

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

12482346921843,2716,54213,08426,16875,233150,466300,932601,864
-1-2-4-8-23-46-92-184-3,271-6,542-13,084-26,168-75,233-150,466-300,932-601,864

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