Q: What are the factor combinations of the number 706,225?

 A:
Positive:   1 x 7062255 x 14124513 x 5432525 x 2824941 x 1722553 x 1332565 x 10865205 x 3445265 x 2665325 x 2173533 x 1325689 x 1025
Negative: -1 x -706225-5 x -141245-13 x -54325-25 x -28249-41 x -17225-53 x -13325-65 x -10865-205 x -3445-265 x -2665-325 x -2173-533 x -1325-689 x -1025


How do I find the factor combinations of the number 706,225?

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 706,225, 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.

1 706,225
-1 -706,225

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 706,225.

Example:
1 x 706,225 = 706,225
and
-1 x -706,225 = 706,225
Notice both answers equal 706,225

With that explanation out of the way, let's continue. Next, we take the number 706,225 and divide it by 2:

706,225 ÷ 2 = 353,112.5

If the quotient is a whole number, then 2 and 353,112.5 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:

1 706,225
-1 -706,225

Now, we try dividing 706,225 by 3:

706,225 ÷ 3 = 235,408.3333

If the quotient is a whole number, then 3 and 235,408.3333 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:

1 706,225
-1 -706,225

Let's try dividing by 4:

706,225 ÷ 4 = 176,556.25

If the quotient is a whole number, then 4 and 176,556.25 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:

1 706,225
-1 706,225
Keep dividing by the next highest number until you cannot divide anymore.

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

1513254153652052653255336891,0251,3252,1732,6653,44510,86513,32517,22528,24954,325141,245706,225
-1-5-13-25-41-53-65-205-265-325-533-689-1,025-1,325-2,173-2,665-3,445-10,865-13,325-17,225-28,249-54,325-141,245-706,225

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