Q: What are the factor combinations of the number 142,636,021?

 A:
Positive:   1 x 14263602111 x 1296691119 x 7507159209 x 682469251 x 5682712719 x 524592761 x 516614769 x 29909
Negative: -1 x -142636021-11 x -12966911-19 x -7507159-209 x -682469-251 x -568271-2719 x -52459-2761 x -51661-4769 x -29909


How do I find the factor combinations of the number 142,636,021?

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 142,636,021, 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.

1 142,636,021
-1 -142,636,021

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 142,636,021.

Example:
1 x 142,636,021 = 142,636,021
and
-1 x -142,636,021 = 142,636,021
Notice both answers equal 142,636,021

With that explanation out of the way, let's continue. Next, we take the number 142,636,021 and divide it by 2:

142,636,021 ÷ 2 = 71,318,010.5

If the quotient is a whole number, then 2 and 71,318,010.5 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:

1 142,636,021
-1 -142,636,021

Now, we try dividing 142,636,021 by 3:

142,636,021 ÷ 3 = 47,545,340.3333

If the quotient is a whole number, then 3 and 47,545,340.3333 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:

1 142,636,021
-1 -142,636,021

Let's try dividing by 4:

142,636,021 ÷ 4 = 35,659,005.25

If the quotient is a whole number, then 4 and 35,659,005.25 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:

1 142,636,021
-1 142,636,021
Keep dividing by the next highest number until you cannot divide anymore.

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

111192092512,7192,7614,76929,90951,66152,459568,271682,4697,507,15912,966,911142,636,021
-1-11-19-209-251-2,719-2,761-4,769-29,909-51,661-52,459-568,271-682,469-7,507,159-12,966,911-142,636,021

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