Q: What are the factor combinations of the number 5,465?

 A:
Positive:   1 x 54655 x 1093
Negative: -1 x -5465-5 x -1093


How do I find the factor combinations of the number 5,465?

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 5,465, 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 5,465
-1 -5,465

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 5,465.

Example:
1 x 5,465 = 5,465
and
-1 x -5,465 = 5,465
Notice both answers equal 5,465

With that explanation out of the way, let's continue. Next, we take the number 5,465 and divide it by 2:

5,465 ÷ 2 = 2,732.5

If the quotient is a whole number, then 2 and 2,732.5 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 5,465
-1 -5,465

Now, we try dividing 5,465 by 3:

5,465 ÷ 3 = 1,821.6667

If the quotient is a whole number, then 3 and 1,821.6667 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 5,465
-1 -5,465

Let's try dividing by 4:

5,465 ÷ 4 = 1,366.25

If the quotient is a whole number, then 4 and 1,366.25 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 5,465
-1 5,465
Keep dividing by the next highest number until you cannot divide anymore.

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

151,0935,465
-1-5-1,093-5,465

More Examples

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