Q: What are the factor combinations of the number 21,002,525?

 A:
Positive:   1 x 210025255 x 420050525 x 84010129 x 72422559 x 355975145 x 144845295 x 71195491 x 42775725 x 289691475 x 142391711 x 122752455 x 8555
Negative: -1 x -21002525-5 x -4200505-25 x -840101-29 x -724225-59 x -355975-145 x -144845-295 x -71195-491 x -42775-725 x -28969-1475 x -14239-1711 x -12275-2455 x -8555


How do I find the factor combinations of the number 21,002,525?

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 21,002,525, 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 21,002,525
-1 -21,002,525

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 21,002,525.

Example:
1 x 21,002,525 = 21,002,525
and
-1 x -21,002,525 = 21,002,525
Notice both answers equal 21,002,525

With that explanation out of the way, let's continue. Next, we take the number 21,002,525 and divide it by 2:

21,002,525 ÷ 2 = 10,501,262.5

If the quotient is a whole number, then 2 and 10,501,262.5 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 21,002,525
-1 -21,002,525

Now, we try dividing 21,002,525 by 3:

21,002,525 ÷ 3 = 7,000,841.6667

If the quotient is a whole number, then 3 and 7,000,841.6667 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 21,002,525
-1 -21,002,525

Let's try dividing by 4:

21,002,525 ÷ 4 = 5,250,631.25

If the quotient is a whole number, then 4 and 5,250,631.25 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 21,002,525
-1 21,002,525
Keep dividing by the next highest number until you cannot divide anymore.

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

152529591452954917251,4751,7112,4558,55512,27514,23928,96942,77571,195144,845355,975724,225840,1014,200,50521,002,525
-1-5-25-29-59-145-295-491-725-1,475-1,711-2,455-8,555-12,275-14,239-28,969-42,775-71,195-144,845-355,975-724,225-840,101-4,200,505-21,002,525

More Examples

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