Q: What are the factor combinations of the number 712,075?

 A:
Positive:   1 x 7120755 x 1424157 x 10172513 x 5477525 x 2848335 x 2034565 x 1095591 x 7825175 x 4069313 x 2275325 x 2191455 x 1565
Negative: -1 x -712075-5 x -142415-7 x -101725-13 x -54775-25 x -28483-35 x -20345-65 x -10955-91 x -7825-175 x -4069-313 x -2275-325 x -2191-455 x -1565


How do I find the factor combinations of the number 712,075?

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 712,075, 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.

1 712,075
-1 -712,075

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 712,075.

Example:
1 x 712,075 = 712,075
and
-1 x -712,075 = 712,075
Notice both answers equal 712,075

With that explanation out of the way, let's continue. Next, we take the number 712,075 and divide it by 2:

712,075 ÷ 2 = 356,037.5

If the quotient is a whole number, then 2 and 356,037.5 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:

1 712,075
-1 -712,075

Now, we try dividing 712,075 by 3:

712,075 ÷ 3 = 237,358.3333

If the quotient is a whole number, then 3 and 237,358.3333 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:

1 712,075
-1 -712,075

Let's try dividing by 4:

712,075 ÷ 4 = 178,018.75

If the quotient is a whole number, then 4 and 178,018.75 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:

1 712,075
-1 712,075
Keep dividing by the next highest number until you cannot divide anymore.

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

15713253565911753133254551,5652,1912,2754,0697,82510,95520,34528,48354,775101,725142,415712,075
-1-5-7-13-25-35-65-91-175-313-325-455-1,565-2,191-2,275-4,069-7,825-10,955-20,345-28,483-54,775-101,725-142,415-712,075

More Examples

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