Q: What are the factor combinations of the number 10,202,225?

 A:
Positive:   1 x 102022255 x 204044511 x 92747523 x 44357525 x 40808955 x 185495115 x 88715253 x 40325275 x 37099575 x 177431265 x 80651613 x 6325
Negative: -1 x -10202225-5 x -2040445-11 x -927475-23 x -443575-25 x -408089-55 x -185495-115 x -88715-253 x -40325-275 x -37099-575 x -17743-1265 x -8065-1613 x -6325


How do I find the factor combinations of the number 10,202,225?

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 10,202,225, 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 10,202,225
-1 -10,202,225

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 10,202,225.

Example:
1 x 10,202,225 = 10,202,225
and
-1 x -10,202,225 = 10,202,225
Notice both answers equal 10,202,225

With that explanation out of the way, let's continue. Next, we take the number 10,202,225 and divide it by 2:

10,202,225 ÷ 2 = 5,101,112.5

If the quotient is a whole number, then 2 and 5,101,112.5 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 10,202,225
-1 -10,202,225

Now, we try dividing 10,202,225 by 3:

10,202,225 ÷ 3 = 3,400,741.6667

If the quotient is a whole number, then 3 and 3,400,741.6667 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 10,202,225
-1 -10,202,225

Let's try dividing by 4:

10,202,225 ÷ 4 = 2,550,556.25

If the quotient is a whole number, then 4 and 2,550,556.25 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 10,202,225
-1 10,202,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15112325551152532755751,2651,6136,3258,06517,74337,09940,32588,715185,495408,089443,575927,4752,040,44510,202,225
-1-5-11-23-25-55-115-253-275-575-1,265-1,613-6,325-8,065-17,743-37,099-40,325-88,715-185,495-408,089-443,575-927,475-2,040,445-10,202,225

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