Q: What are the factor combinations of the number 21,434,299?

 A:
Positive:   1 x 2143429919 x 112812131 x 691429151 x 141949241 x 88939589 x 363912869 x 74714579 x 4681
Negative: -1 x -21434299-19 x -1128121-31 x -691429-151 x -141949-241 x -88939-589 x -36391-2869 x -7471-4579 x -4681


How do I find the factor combinations of the number 21,434,299?

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 21,434,299, 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 21,434,299
-1 -21,434,299

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 21,434,299.

Example:
1 x 21,434,299 = 21,434,299
and
-1 x -21,434,299 = 21,434,299
Notice both answers equal 21,434,299

With that explanation out of the way, let's continue. Next, we take the number 21,434,299 and divide it by 2:

21,434,299 ÷ 2 = 10,717,149.5

If the quotient is a whole number, then 2 and 10,717,149.5 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 21,434,299
-1 -21,434,299

Now, we try dividing 21,434,299 by 3:

21,434,299 ÷ 3 = 7,144,766.3333

If the quotient is a whole number, then 3 and 7,144,766.3333 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 21,434,299
-1 -21,434,299

Let's try dividing by 4:

21,434,299 ÷ 4 = 5,358,574.75

If the quotient is a whole number, then 4 and 5,358,574.75 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 21,434,299
-1 21,434,299
Keep dividing by the next highest number until you cannot divide anymore.

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

119311512415892,8694,5794,6817,47136,39188,939141,949691,4291,128,12121,434,299
-1-19-31-151-241-589-2,869-4,579-4,681-7,471-36,391-88,939-141,949-691,429-1,128,121-21,434,299

More Examples

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