Q: What are the factor combinations of the number 53,396?

 A:
Positive:   1 x 533962 x 266984 x 133497 x 762814 x 381428 x 1907
Negative: -1 x -53396-2 x -26698-4 x -13349-7 x -7628-14 x -3814-28 x -1907


How do I find the factor combinations of the number 53,396?

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 53,396, 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 53,396
-1 -53,396

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 53,396.

Example:
1 x 53,396 = 53,396
and
-1 x -53,396 = 53,396
Notice both answers equal 53,396

With that explanation out of the way, let's continue. Next, we take the number 53,396 and divide it by 2:

53,396 ÷ 2 = 26,698

If the quotient is a whole number, then 2 and 26,698 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 26,698 53,396
-1 -2 -26,698 -53,396

Now, we try dividing 53,396 by 3:

53,396 ÷ 3 = 17,798.6667

If the quotient is a whole number, then 3 and 17,798.6667 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 2 26,698 53,396
-1 -2 -26,698 -53,396

Let's try dividing by 4:

53,396 ÷ 4 = 13,349

If the quotient is a whole number, then 4 and 13,349 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 4 13,349 26,698 53,396
-1 -2 -4 -13,349 -26,698 53,396
Keep dividing by the next highest number until you cannot divide anymore.

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

124714281,9073,8147,62813,34926,69853,396
-1-2-4-7-14-28-1,907-3,814-7,628-13,349-26,698-53,396

More Examples

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