Q: What are the factor combinations of the number 73,075,821?

 A:
Positive:   1 x 730758213 x 243586077 x 1043940313 x 562121721 x 347980139 x 187373991 x 803031273 x 267677
Negative: -1 x -73075821-3 x -24358607-7 x -10439403-13 x -5621217-21 x -3479801-39 x -1873739-91 x -803031-273 x -267677


How do I find the factor combinations of the number 73,075,821?

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 73,075,821, 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 73,075,821
-1 -73,075,821

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 73,075,821.

Example:
1 x 73,075,821 = 73,075,821
and
-1 x -73,075,821 = 73,075,821
Notice both answers equal 73,075,821

With that explanation out of the way, let's continue. Next, we take the number 73,075,821 and divide it by 2:

73,075,821 ÷ 2 = 36,537,910.5

If the quotient is a whole number, then 2 and 36,537,910.5 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 73,075,821
-1 -73,075,821

Now, we try dividing 73,075,821 by 3:

73,075,821 ÷ 3 = 24,358,607

If the quotient is a whole number, then 3 and 24,358,607 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 3 24,358,607 73,075,821
-1 -3 -24,358,607 -73,075,821

Let's try dividing by 4:

73,075,821 ÷ 4 = 18,268,955.25

If the quotient is a whole number, then 4 and 18,268,955.25 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 3 24,358,607 73,075,821
-1 -3 -24,358,607 73,075,821
Keep dividing by the next highest number until you cannot divide anymore.

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

13713213991273267,677803,0311,873,7393,479,8015,621,21710,439,40324,358,60773,075,821
-1-3-7-13-21-39-91-273-267,677-803,031-1,873,739-3,479,801-5,621,217-10,439,403-24,358,607-73,075,821

More Examples

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