Q: What are the factor combinations of the number 146,244?

 A:
Positive:   1 x 1462442 x 731223 x 487484 x 365616 x 243747 x 2089212 x 1218714 x 1044621 x 696428 x 522342 x 348284 x 1741
Negative: -1 x -146244-2 x -73122-3 x -48748-4 x -36561-6 x -24374-7 x -20892-12 x -12187-14 x -10446-21 x -6964-28 x -5223-42 x -3482-84 x -1741


How do I find the factor combinations of the number 146,244?

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 146,244, 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.

1 146,244
-1 -146,244

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 146,244.

Example:
1 x 146,244 = 146,244
and
-1 x -146,244 = 146,244
Notice both answers equal 146,244

With that explanation out of the way, let's continue. Next, we take the number 146,244 and divide it by 2:

146,244 ÷ 2 = 73,122

If the quotient is a whole number, then 2 and 73,122 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 73,122 146,244
-1 -2 -73,122 -146,244

Now, we try dividing 146,244 by 3:

146,244 ÷ 3 = 48,748

If the quotient is a whole number, then 3 and 48,748 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 48,748 73,122 146,244
-1 -2 -3 -48,748 -73,122 -146,244

Let's try dividing by 4:

146,244 ÷ 4 = 36,561

If the quotient is a whole number, then 4 and 36,561 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 4 36,561 48,748 73,122 146,244
-1 -2 -3 -4 -36,561 -48,748 -73,122 146,244
Keep dividing by the next highest number until you cannot divide anymore.

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

1234671214212842841,7413,4825,2236,96410,44612,18720,89224,37436,56148,74873,122146,244
-1-2-3-4-6-7-12-14-21-28-42-84-1,741-3,482-5,223-6,964-10,446-12,187-20,892-24,374-36,561-48,748-73,122-146,244

More Examples

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