Q: What are the factor combinations of the number 98,735?

 A:
Positive:   1 x 987355 x 197477 x 1410513 x 759531 x 318535 x 282149 x 201565 x 151991 x 1085155 x 637217 x 455245 x 403
Negative: -1 x -98735-5 x -19747-7 x -14105-13 x -7595-31 x -3185-35 x -2821-49 x -2015-65 x -1519-91 x -1085-155 x -637-217 x -455-245 x -403


How do I find the factor combinations of the number 98,735?

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 98,735, 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 98,735
-1 -98,735

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 98,735.

Example:
1 x 98,735 = 98,735
and
-1 x -98,735 = 98,735
Notice both answers equal 98,735

With that explanation out of the way, let's continue. Next, we take the number 98,735 and divide it by 2:

98,735 ÷ 2 = 49,367.5

If the quotient is a whole number, then 2 and 49,367.5 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 98,735
-1 -98,735

Now, we try dividing 98,735 by 3:

98,735 ÷ 3 = 32,911.6667

If the quotient is a whole number, then 3 and 32,911.6667 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 98,735
-1 -98,735

Let's try dividing by 4:

98,735 ÷ 4 = 24,683.75

If the quotient is a whole number, then 4 and 24,683.75 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 98,735
-1 98,735
Keep dividing by the next highest number until you cannot divide anymore.

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

1571331354965911552172454034556371,0851,5192,0152,8213,1857,59514,10519,74798,735
-1-5-7-13-31-35-49-65-91-155-217-245-403-455-637-1,085-1,519-2,015-2,821-3,185-7,595-14,105-19,747-98,735

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