Q: What are the factor combinations of the number 221,033,267?

 A:
Positive:   1 x 2210332677 x 3157618113 x 1700255949 x 451088353 x 417043991 x 2428937371 x 595777637 x 346991689 x 3208032597 x 851114823 x 458296547 x 33761
Negative: -1 x -221033267-7 x -31576181-13 x -17002559-49 x -4510883-53 x -4170439-91 x -2428937-371 x -595777-637 x -346991-689 x -320803-2597 x -85111-4823 x -45829-6547 x -33761


How do I find the factor combinations of the number 221,033,267?

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 221,033,267, 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.

1 221,033,267
-1 -221,033,267

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 221,033,267.

Example:
1 x 221,033,267 = 221,033,267
and
-1 x -221,033,267 = 221,033,267
Notice both answers equal 221,033,267

With that explanation out of the way, let's continue. Next, we take the number 221,033,267 and divide it by 2:

221,033,267 ÷ 2 = 110,516,633.5

If the quotient is a whole number, then 2 and 110,516,633.5 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:

1 221,033,267
-1 -221,033,267

Now, we try dividing 221,033,267 by 3:

221,033,267 ÷ 3 = 73,677,755.6667

If the quotient is a whole number, then 3 and 73,677,755.6667 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:

1 221,033,267
-1 -221,033,267

Let's try dividing by 4:

221,033,267 ÷ 4 = 55,258,316.75

If the quotient is a whole number, then 4 and 55,258,316.75 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:

1 221,033,267
-1 221,033,267
Keep dividing by the next highest number until you cannot divide anymore.

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

17134953913716376892,5974,8236,54733,76145,82985,111320,803346,991595,7772,428,9374,170,4394,510,88317,002,55931,576,181221,033,267
-1-7-13-49-53-91-371-637-689-2,597-4,823-6,547-33,761-45,829-85,111-320,803-346,991-595,777-2,428,937-4,170,439-4,510,883-17,002,559-31,576,181-221,033,267

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