Q: What are the factor combinations of the number 53,977?

 A:
Positive:   1 x 539777 x 771111 x 490777 x 701
Negative: -1 x -53977-7 x -7711-11 x -4907-77 x -701


How do I find the factor combinations of the number 53,977?

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 53,977, 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 53,977
-1 -53,977

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 53,977.

Example:
1 x 53,977 = 53,977
and
-1 x -53,977 = 53,977
Notice both answers equal 53,977

With that explanation out of the way, let's continue. Next, we take the number 53,977 and divide it by 2:

53,977 ÷ 2 = 26,988.5

If the quotient is a whole number, then 2 and 26,988.5 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 53,977
-1 -53,977

Now, we try dividing 53,977 by 3:

53,977 ÷ 3 = 17,992.3333

If the quotient is a whole number, then 3 and 17,992.3333 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 53,977
-1 -53,977

Let's try dividing by 4:

53,977 ÷ 4 = 13,494.25

If the quotient is a whole number, then 4 and 13,494.25 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 53,977
-1 53,977
Keep dividing by the next highest number until you cannot divide anymore.

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

1711777014,9077,71153,977
-1-7-11-77-701-4,907-7,711-53,977

More Examples

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