Q: What are the factor combinations of the number 25,461,625?

 A:
Positive:   1 x 254616255 x 50923257 x 363737525 x 101846535 x 72747549 x 519625125 x 203693175 x 145495245 x 103925875 x 290991225 x 207854157 x 6125
Negative: -1 x -25461625-5 x -5092325-7 x -3637375-25 x -1018465-35 x -727475-49 x -519625-125 x -203693-175 x -145495-245 x -103925-875 x -29099-1225 x -20785-4157 x -6125


How do I find the factor combinations of the number 25,461,625?

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 25,461,625, 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 25,461,625
-1 -25,461,625

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 25,461,625.

Example:
1 x 25,461,625 = 25,461,625
and
-1 x -25,461,625 = 25,461,625
Notice both answers equal 25,461,625

With that explanation out of the way, let's continue. Next, we take the number 25,461,625 and divide it by 2:

25,461,625 ÷ 2 = 12,730,812.5

If the quotient is a whole number, then 2 and 12,730,812.5 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 25,461,625
-1 -25,461,625

Now, we try dividing 25,461,625 by 3:

25,461,625 ÷ 3 = 8,487,208.3333

If the quotient is a whole number, then 3 and 8,487,208.3333 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 25,461,625
-1 -25,461,625

Let's try dividing by 4:

25,461,625 ÷ 4 = 6,365,406.25

If the quotient is a whole number, then 4 and 6,365,406.25 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 25,461,625
-1 25,461,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1572535491251752458751,2254,1576,12520,78529,099103,925145,495203,693519,625727,4751,018,4653,637,3755,092,32525,461,625
-1-5-7-25-35-49-125-175-245-875-1,225-4,157-6,125-20,785-29,099-103,925-145,495-203,693-519,625-727,475-1,018,465-3,637,375-5,092,325-25,461,625

More Examples

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