Q: What are the factor combinations of the number 23,164,075?

 A:
Positive:   1 x 231640755 x 463281511 x 210582525 x 92656355 x 421165131 x 176825275 x 84233643 x 36025655 x 353651441 x 160753215 x 72053275 x 7073
Negative: -1 x -23164075-5 x -4632815-11 x -2105825-25 x -926563-55 x -421165-131 x -176825-275 x -84233-643 x -36025-655 x -35365-1441 x -16075-3215 x -7205-3275 x -7073


How do I find the factor combinations of the number 23,164,075?

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 23,164,075, 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 23,164,075
-1 -23,164,075

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 23,164,075.

Example:
1 x 23,164,075 = 23,164,075
and
-1 x -23,164,075 = 23,164,075
Notice both answers equal 23,164,075

With that explanation out of the way, let's continue. Next, we take the number 23,164,075 and divide it by 2:

23,164,075 ÷ 2 = 11,582,037.5

If the quotient is a whole number, then 2 and 11,582,037.5 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 23,164,075
-1 -23,164,075

Now, we try dividing 23,164,075 by 3:

23,164,075 ÷ 3 = 7,721,358.3333

If the quotient is a whole number, then 3 and 7,721,358.3333 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 23,164,075
-1 -23,164,075

Let's try dividing by 4:

23,164,075 ÷ 4 = 5,791,018.75

If the quotient is a whole number, then 4 and 5,791,018.75 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 23,164,075
-1 23,164,075
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551312756436551,4413,2153,2757,0737,20516,07535,36536,02584,233176,825421,165926,5632,105,8254,632,81523,164,075
-1-5-11-25-55-131-275-643-655-1,441-3,215-3,275-7,073-7,205-16,075-35,365-36,025-84,233-176,825-421,165-926,563-2,105,825-4,632,815-23,164,075

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