Q: What are the factor combinations of the number 1,724,125?

 A:
Positive:   1 x 17241255 x 34482513 x 13262525 x 6896565 x 26525125 x 13793325 x 53051061 x 1625
Negative: -1 x -1724125-5 x -344825-13 x -132625-25 x -68965-65 x -26525-125 x -13793-325 x -5305-1061 x -1625


How do I find the factor combinations of the number 1,724,125?

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 1,724,125, 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 1,724,125
-1 -1,724,125

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 1,724,125.

Example:
1 x 1,724,125 = 1,724,125
and
-1 x -1,724,125 = 1,724,125
Notice both answers equal 1,724,125

With that explanation out of the way, let's continue. Next, we take the number 1,724,125 and divide it by 2:

1,724,125 ÷ 2 = 862,062.5

If the quotient is a whole number, then 2 and 862,062.5 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 1,724,125
-1 -1,724,125

Now, we try dividing 1,724,125 by 3:

1,724,125 ÷ 3 = 574,708.3333

If the quotient is a whole number, then 3 and 574,708.3333 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 1,724,125
-1 -1,724,125

Let's try dividing by 4:

1,724,125 ÷ 4 = 431,031.25

If the quotient is a whole number, then 4 and 431,031.25 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 1,724,125
-1 1,724,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151325651253251,0611,6255,30513,79326,52568,965132,625344,8251,724,125
-1-5-13-25-65-125-325-1,061-1,625-5,305-13,793-26,525-68,965-132,625-344,825-1,724,125

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