Q: What are the factor combinations of the number 45,221,033?

 A:
Positive:   1 x 4522103311 x 411100313 x 347854131 x 1458743101 x 447733143 x 316231341 x 132613403 x 1122111111 x 407031313 x 344413131 x 144434433 x 10201
Negative: -1 x -45221033-11 x -4111003-13 x -3478541-31 x -1458743-101 x -447733-143 x -316231-341 x -132613-403 x -112211-1111 x -40703-1313 x -34441-3131 x -14443-4433 x -10201


How do I find the factor combinations of the number 45,221,033?

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 45,221,033, 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 45,221,033
-1 -45,221,033

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 45,221,033.

Example:
1 x 45,221,033 = 45,221,033
and
-1 x -45,221,033 = 45,221,033
Notice both answers equal 45,221,033

With that explanation out of the way, let's continue. Next, we take the number 45,221,033 and divide it by 2:

45,221,033 ÷ 2 = 22,610,516.5

If the quotient is a whole number, then 2 and 22,610,516.5 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 45,221,033
-1 -45,221,033

Now, we try dividing 45,221,033 by 3:

45,221,033 ÷ 3 = 15,073,677.6667

If the quotient is a whole number, then 3 and 15,073,677.6667 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 45,221,033
-1 -45,221,033

Let's try dividing by 4:

45,221,033 ÷ 4 = 11,305,258.25

If the quotient is a whole number, then 4 and 11,305,258.25 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 45,221,033
-1 45,221,033
Keep dividing by the next highest number until you cannot divide anymore.

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

11113311011433414031,1111,3133,1314,43310,20114,44334,44140,703112,211132,613316,231447,7331,458,7433,478,5414,111,00345,221,033
-1-11-13-31-101-143-341-403-1,111-1,313-3,131-4,433-10,201-14,443-34,441-40,703-112,211-132,613-316,231-447,733-1,458,743-3,478,541-4,111,003-45,221,033

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