Q: What are the factor combinations of the number 25,355,309?

 A:
Positive:   1 x 253553097 x 362218729 x 87432159 x 42975173 x 347333203 x 124903413 x 61393511 x 49619841 x 301491711 x 148192117 x 119774307 x 5887
Negative: -1 x -25355309-7 x -3622187-29 x -874321-59 x -429751-73 x -347333-203 x -124903-413 x -61393-511 x -49619-841 x -30149-1711 x -14819-2117 x -11977-4307 x -5887


How do I find the factor combinations of the number 25,355,309?

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 25,355,309, 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 25,355,309
-1 -25,355,309

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 25,355,309.

Example:
1 x 25,355,309 = 25,355,309
and
-1 x -25,355,309 = 25,355,309
Notice both answers equal 25,355,309

With that explanation out of the way, let's continue. Next, we take the number 25,355,309 and divide it by 2:

25,355,309 ÷ 2 = 12,677,654.5

If the quotient is a whole number, then 2 and 12,677,654.5 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 25,355,309
-1 -25,355,309

Now, we try dividing 25,355,309 by 3:

25,355,309 ÷ 3 = 8,451,769.6667

If the quotient is a whole number, then 3 and 8,451,769.6667 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 25,355,309
-1 -25,355,309

Let's try dividing by 4:

25,355,309 ÷ 4 = 6,338,827.25

If the quotient is a whole number, then 4 and 6,338,827.25 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 25,355,309
-1 25,355,309
Keep dividing by the next highest number until you cannot divide anymore.

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

172959732034135118411,7112,1174,3075,88711,97714,81930,14949,61961,393124,903347,333429,751874,3213,622,18725,355,309
-1-7-29-59-73-203-413-511-841-1,711-2,117-4,307-5,887-11,977-14,819-30,149-49,619-61,393-124,903-347,333-429,751-874,321-3,622,187-25,355,309

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