Q: What are the factor combinations of the number 65,820?

 A:
Positive:   1 x 658202 x 329103 x 219404 x 164555 x 131646 x 1097010 x 658212 x 548515 x 438820 x 329130 x 219460 x 1097
Negative: -1 x -65820-2 x -32910-3 x -21940-4 x -16455-5 x -13164-6 x -10970-10 x -6582-12 x -5485-15 x -4388-20 x -3291-30 x -2194-60 x -1097


How do I find the factor combinations of the number 65,820?

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 65,820, 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 65,820
-1 -65,820

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 65,820.

Example:
1 x 65,820 = 65,820
and
-1 x -65,820 = 65,820
Notice both answers equal 65,820

With that explanation out of the way, let's continue. Next, we take the number 65,820 and divide it by 2:

65,820 ÷ 2 = 32,910

If the quotient is a whole number, then 2 and 32,910 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 32,910 65,820
-1 -2 -32,910 -65,820

Now, we try dividing 65,820 by 3:

65,820 ÷ 3 = 21,940

If the quotient is a whole number, then 3 and 21,940 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 21,940 32,910 65,820
-1 -2 -3 -21,940 -32,910 -65,820

Let's try dividing by 4:

65,820 ÷ 4 = 16,455

If the quotient is a whole number, then 4 and 16,455 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 16,455 21,940 32,910 65,820
-1 -2 -3 -4 -16,455 -21,940 -32,910 65,820
Keep dividing by the next highest number until you cannot divide anymore.

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

1234561012152030601,0972,1943,2914,3885,4856,58210,97013,16416,45521,94032,91065,820
-1-2-3-4-5-6-10-12-15-20-30-60-1,097-2,194-3,291-4,388-5,485-6,582-10,970-13,164-16,455-21,940-32,910-65,820

More Examples

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