Q: What are the factor combinations of the number 285,462?

 A:
Positive:   1 x 2854622 x 1427313 x 951546 x 475779 x 3171818 x 15859
Negative: -1 x -285462-2 x -142731-3 x -95154-6 x -47577-9 x -31718-18 x -15859


How do I find the factor combinations of the number 285,462?

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 285,462, 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.

1 285,462
-1 -285,462

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 285,462.

Example:
1 x 285,462 = 285,462
and
-1 x -285,462 = 285,462
Notice both answers equal 285,462

With that explanation out of the way, let's continue. Next, we take the number 285,462 and divide it by 2:

285,462 ÷ 2 = 142,731

If the quotient is a whole number, then 2 and 142,731 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 2 142,731 285,462
-1 -2 -142,731 -285,462

Now, we try dividing 285,462 by 3:

285,462 ÷ 3 = 95,154

If the quotient is a whole number, then 3 and 95,154 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 95,154 142,731 285,462
-1 -2 -3 -95,154 -142,731 -285,462

Let's try dividing by 4:

285,462 ÷ 4 = 71,365.5

If the quotient is a whole number, then 4 and 71,365.5 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 2 3 95,154 142,731 285,462
-1 -2 -3 -95,154 -142,731 285,462
Keep dividing by the next highest number until you cannot divide anymore.

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

123691815,85931,71847,57795,154142,731285,462
-1-2-3-6-9-18-15,859-31,718-47,577-95,154-142,731-285,462

More Examples

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