Q: What are the factor combinations of the number 153,978?

 A:
Positive:   1 x 1539782 x 769893 x 513266 x 2566311 x 1399822 x 699933 x 466666 x 2333
Negative: -1 x -153978-2 x -76989-3 x -51326-6 x -25663-11 x -13998-22 x -6999-33 x -4666-66 x -2333


How do I find the factor combinations of the number 153,978?

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 153,978, 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.

1 153,978
-1 -153,978

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 153,978.

Example:
1 x 153,978 = 153,978
and
-1 x -153,978 = 153,978
Notice both answers equal 153,978

With that explanation out of the way, let's continue. Next, we take the number 153,978 and divide it by 2:

153,978 ÷ 2 = 76,989

If the quotient is a whole number, then 2 and 76,989 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 76,989 153,978
-1 -2 -76,989 -153,978

Now, we try dividing 153,978 by 3:

153,978 ÷ 3 = 51,326

If the quotient is a whole number, then 3 and 51,326 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 3 51,326 76,989 153,978
-1 -2 -3 -51,326 -76,989 -153,978

Let's try dividing by 4:

153,978 ÷ 4 = 38,494.5

If the quotient is a whole number, then 4 and 38,494.5 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 2 3 51,326 76,989 153,978
-1 -2 -3 -51,326 -76,989 153,978
Keep dividing by the next highest number until you cannot divide anymore.

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

1236112233662,3334,6666,99913,99825,66351,32676,989153,978
-1-2-3-6-11-22-33-66-2,333-4,666-6,999-13,998-25,663-51,326-76,989-153,978

More Examples

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