Q: What are the factor combinations of the number 258,628,225?

 A:
Positive:   1 x 2586282255 x 5172564517 x 1521342525 x 1034512979 x 327377585 x 3042685395 x 654755425 x 6085371343 x 1925751975 x 1309516715 x 385157703 x 33575
Negative: -1 x -258628225-5 x -51725645-17 x -15213425-25 x -10345129-79 x -3273775-85 x -3042685-395 x -654755-425 x -608537-1343 x -192575-1975 x -130951-6715 x -38515-7703 x -33575


How do I find the factor combinations of the number 258,628,225?

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 258,628,225, 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.

1 258,628,225
-1 -258,628,225

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 258,628,225.

Example:
1 x 258,628,225 = 258,628,225
and
-1 x -258,628,225 = 258,628,225
Notice both answers equal 258,628,225

With that explanation out of the way, let's continue. Next, we take the number 258,628,225 and divide it by 2:

258,628,225 ÷ 2 = 129,314,112.5

If the quotient is a whole number, then 2 and 129,314,112.5 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:

1 258,628,225
-1 -258,628,225

Now, we try dividing 258,628,225 by 3:

258,628,225 ÷ 3 = 86,209,408.3333

If the quotient is a whole number, then 3 and 86,209,408.3333 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:

1 258,628,225
-1 -258,628,225

Let's try dividing by 4:

258,628,225 ÷ 4 = 64,657,056.25

If the quotient is a whole number, then 4 and 64,657,056.25 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:

1 258,628,225
-1 258,628,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15172579853954251,3431,9756,7157,70333,57538,515130,951192,575608,537654,7553,042,6853,273,77510,345,12915,213,42551,725,645258,628,225
-1-5-17-25-79-85-395-425-1,343-1,975-6,715-7,703-33,575-38,515-130,951-192,575-608,537-654,755-3,042,685-3,273,775-10,345,129-15,213,425-51,725,645-258,628,225

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