Q: What are the factor combinations of the number 2,142,665?

 A:
Positive:   1 x 21426655 x 4285337 x 30609529 x 7388535 x 61219145 x 14777203 x 105551015 x 2111
Negative: -1 x -2142665-5 x -428533-7 x -306095-29 x -73885-35 x -61219-145 x -14777-203 x -10555-1015 x -2111


How do I find the factor combinations of the number 2,142,665?

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 2,142,665, 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 2,142,665
-1 -2,142,665

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 2,142,665.

Example:
1 x 2,142,665 = 2,142,665
and
-1 x -2,142,665 = 2,142,665
Notice both answers equal 2,142,665

With that explanation out of the way, let's continue. Next, we take the number 2,142,665 and divide it by 2:

2,142,665 ÷ 2 = 1,071,332.5

If the quotient is a whole number, then 2 and 1,071,332.5 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 2,142,665
-1 -2,142,665

Now, we try dividing 2,142,665 by 3:

2,142,665 ÷ 3 = 714,221.6667

If the quotient is a whole number, then 3 and 714,221.6667 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 2,142,665
-1 -2,142,665

Let's try dividing by 4:

2,142,665 ÷ 4 = 535,666.25

If the quotient is a whole number, then 4 and 535,666.25 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 2,142,665
-1 2,142,665
Keep dividing by the next highest number until you cannot divide anymore.

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

15729351452031,0152,11110,55514,77761,21973,885306,095428,5332,142,665
-1-5-7-29-35-145-203-1,015-2,111-10,555-14,777-61,219-73,885-306,095-428,533-2,142,665

More Examples

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