Q: What are the factor combinations of the number 221,448?

 A:
Positive:   1 x 2214482 x 1107243 x 738164 x 553626 x 369088 x 2768112 x 1845424 x 9227
Negative: -1 x -221448-2 x -110724-3 x -73816-4 x -55362-6 x -36908-8 x -27681-12 x -18454-24 x -9227


How do I find the factor combinations of the number 221,448?

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 221,448, 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.

1 221,448
-1 -221,448

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 221,448.

Example:
1 x 221,448 = 221,448
and
-1 x -221,448 = 221,448
Notice both answers equal 221,448

With that explanation out of the way, let's continue. Next, we take the number 221,448 and divide it by 2:

221,448 ÷ 2 = 110,724

If the quotient is a whole number, then 2 and 110,724 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 2 110,724 221,448
-1 -2 -110,724 -221,448

Now, we try dividing 221,448 by 3:

221,448 ÷ 3 = 73,816

If the quotient is a whole number, then 3 and 73,816 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 73,816 110,724 221,448
-1 -2 -3 -73,816 -110,724 -221,448

Let's try dividing by 4:

221,448 ÷ 4 = 55,362

If the quotient is a whole number, then 4 and 55,362 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 55,362 73,816 110,724 221,448
-1 -2 -3 -4 -55,362 -73,816 -110,724 221,448
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812249,22718,45427,68136,90855,36273,816110,724221,448
-1-2-3-4-6-8-12-24-9,227-18,454-27,681-36,908-55,362-73,816-110,724-221,448

More Examples

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