Q: What are the factor combinations of the number 224,154,421?

 A:
Positive:   1 x 22415442141 x 546718147 x 476924389 x 25185891307 x 1715031927 x 1163233649 x 614294183 x 53587
Negative: -1 x -224154421-41 x -5467181-47 x -4769243-89 x -2518589-1307 x -171503-1927 x -116323-3649 x -61429-4183 x -53587


How do I find the factor combinations of the number 224,154,421?

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 224,154,421, 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.

1 224,154,421
-1 -224,154,421

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 224,154,421.

Example:
1 x 224,154,421 = 224,154,421
and
-1 x -224,154,421 = 224,154,421
Notice both answers equal 224,154,421

With that explanation out of the way, let's continue. Next, we take the number 224,154,421 and divide it by 2:

224,154,421 ÷ 2 = 112,077,210.5

If the quotient is a whole number, then 2 and 112,077,210.5 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:

1 224,154,421
-1 -224,154,421

Now, we try dividing 224,154,421 by 3:

224,154,421 ÷ 3 = 74,718,140.3333

If the quotient is a whole number, then 3 and 74,718,140.3333 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:

1 224,154,421
-1 -224,154,421

Let's try dividing by 4:

224,154,421 ÷ 4 = 56,038,605.25

If the quotient is a whole number, then 4 and 56,038,605.25 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:

1 224,154,421
-1 224,154,421
Keep dividing by the next highest number until you cannot divide anymore.

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

14147891,3071,9273,6494,18353,58761,429116,323171,5032,518,5894,769,2435,467,181224,154,421
-1-41-47-89-1,307-1,927-3,649-4,183-53,587-61,429-116,323-171,503-2,518,589-4,769,243-5,467,181-224,154,421

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