Q: What are the factor combinations of the number 20,100,145?

 A:
Positive:   1 x 201001455 x 402002913 x 154616565 x 309233109 x 184405545 x 368811417 x 141852837 x 7085
Negative: -1 x -20100145-5 x -4020029-13 x -1546165-65 x -309233-109 x -184405-545 x -36881-1417 x -14185-2837 x -7085


How do I find the factor combinations of the number 20,100,145?

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 20,100,145, 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 20,100,145
-1 -20,100,145

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 20,100,145.

Example:
1 x 20,100,145 = 20,100,145
and
-1 x -20,100,145 = 20,100,145
Notice both answers equal 20,100,145

With that explanation out of the way, let's continue. Next, we take the number 20,100,145 and divide it by 2:

20,100,145 ÷ 2 = 10,050,072.5

If the quotient is a whole number, then 2 and 10,050,072.5 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 20,100,145
-1 -20,100,145

Now, we try dividing 20,100,145 by 3:

20,100,145 ÷ 3 = 6,700,048.3333

If the quotient is a whole number, then 3 and 6,700,048.3333 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 20,100,145
-1 -20,100,145

Let's try dividing by 4:

20,100,145 ÷ 4 = 5,025,036.25

If the quotient is a whole number, then 4 and 5,025,036.25 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 20,100,145
-1 20,100,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1513651095451,4172,8377,08514,18536,881184,405309,2331,546,1654,020,02920,100,145
-1-5-13-65-109-545-1,417-2,837-7,085-14,185-36,881-184,405-309,233-1,546,165-4,020,029-20,100,145

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