Q: What are the factor combinations of the number 45,103?

 A:
Positive:   1 x 4510323 x 196137 x 121953 x 851
Negative: -1 x -45103-23 x -1961-37 x -1219-53 x -851


How do I find the factor combinations of the number 45,103?

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 45,103, 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 45,103
-1 -45,103

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 45,103.

Example:
1 x 45,103 = 45,103
and
-1 x -45,103 = 45,103
Notice both answers equal 45,103

With that explanation out of the way, let's continue. Next, we take the number 45,103 and divide it by 2:

45,103 ÷ 2 = 22,551.5

If the quotient is a whole number, then 2 and 22,551.5 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 45,103
-1 -45,103

Now, we try dividing 45,103 by 3:

45,103 ÷ 3 = 15,034.3333

If the quotient is a whole number, then 3 and 15,034.3333 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 45,103
-1 -45,103

Let's try dividing by 4:

45,103 ÷ 4 = 11,275.75

If the quotient is a whole number, then 4 and 11,275.75 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 45,103
-1 45,103
Keep dividing by the next highest number until you cannot divide anymore.

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

12337538511,2191,96145,103
-1-23-37-53-851-1,219-1,961-45,103

More Examples

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