Q: What are the factor combinations of the number 21,400,015?

 A:
Positive:   1 x 214000155 x 42800037 x 305714513 x 164615535 x 61142949 x 43673565 x 32923191 x 235165245 x 87347455 x 47033637 x 335953185 x 6719
Negative: -1 x -21400015-5 x -4280003-7 x -3057145-13 x -1646155-35 x -611429-49 x -436735-65 x -329231-91 x -235165-245 x -87347-455 x -47033-637 x -33595-3185 x -6719


How do I find the factor combinations of the number 21,400,015?

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 21,400,015, 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 21,400,015
-1 -21,400,015

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 21,400,015.

Example:
1 x 21,400,015 = 21,400,015
and
-1 x -21,400,015 = 21,400,015
Notice both answers equal 21,400,015

With that explanation out of the way, let's continue. Next, we take the number 21,400,015 and divide it by 2:

21,400,015 ÷ 2 = 10,700,007.5

If the quotient is a whole number, then 2 and 10,700,007.5 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 21,400,015
-1 -21,400,015

Now, we try dividing 21,400,015 by 3:

21,400,015 ÷ 3 = 7,133,338.3333

If the quotient is a whole number, then 3 and 7,133,338.3333 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 21,400,015
-1 -21,400,015

Let's try dividing by 4:

21,400,015 ÷ 4 = 5,350,003.75

If the quotient is a whole number, then 4 and 5,350,003.75 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 21,400,015
-1 21,400,015
Keep dividing by the next highest number until you cannot divide anymore.

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

15713354965912454556373,1856,71933,59547,03387,347235,165329,231436,735611,4291,646,1553,057,1454,280,00321,400,015
-1-5-7-13-35-49-65-91-245-455-637-3,185-6,719-33,595-47,033-87,347-235,165-329,231-436,735-611,429-1,646,155-3,057,145-4,280,003-21,400,015

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