Q: What are the factor combinations of the number 448,060?

 A:
Positive:   1 x 4480602 x 2240304 x 1120155 x 8961210 x 4480620 x 2240343 x 1042086 x 5210172 x 2605215 x 2084430 x 1042521 x 860
Negative: -1 x -448060-2 x -224030-4 x -112015-5 x -89612-10 x -44806-20 x -22403-43 x -10420-86 x -5210-172 x -2605-215 x -2084-430 x -1042-521 x -860


How do I find the factor combinations of the number 448,060?

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 448,060, 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.

1 448,060
-1 -448,060

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 448,060.

Example:
1 x 448,060 = 448,060
and
-1 x -448,060 = 448,060
Notice both answers equal 448,060

With that explanation out of the way, let's continue. Next, we take the number 448,060 and divide it by 2:

448,060 ÷ 2 = 224,030

If the quotient is a whole number, then 2 and 224,030 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 2 224,030 448,060
-1 -2 -224,030 -448,060

Now, we try dividing 448,060 by 3:

448,060 ÷ 3 = 149,353.3333

If the quotient is a whole number, then 3 and 149,353.3333 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 2 224,030 448,060
-1 -2 -224,030 -448,060

Let's try dividing by 4:

448,060 ÷ 4 = 112,015

If the quotient is a whole number, then 4 and 112,015 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 4 112,015 224,030 448,060
-1 -2 -4 -112,015 -224,030 448,060
Keep dividing by the next highest number until you cannot divide anymore.

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

1245102043861722154305218601,0422,0842,6055,21010,42022,40344,80689,612112,015224,030448,060
-1-2-4-5-10-20-43-86-172-215-430-521-860-1,042-2,084-2,605-5,210-10,420-22,403-44,806-89,612-112,015-224,030-448,060

More Examples

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