Q: What are the factor combinations of the number 178,475?

 A:
Positive:   1 x 1784755 x 3569511 x 1622525 x 713955 x 324559 x 3025121 x 1475275 x 649295 x 605
Negative: -1 x -178475-5 x -35695-11 x -16225-25 x -7139-55 x -3245-59 x -3025-121 x -1475-275 x -649-295 x -605


How do I find the factor combinations of the number 178,475?

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 178,475, 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.

1 178,475
-1 -178,475

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 178,475.

Example:
1 x 178,475 = 178,475
and
-1 x -178,475 = 178,475
Notice both answers equal 178,475

With that explanation out of the way, let's continue. Next, we take the number 178,475 and divide it by 2:

178,475 ÷ 2 = 89,237.5

If the quotient is a whole number, then 2 and 89,237.5 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:

1 178,475
-1 -178,475

Now, we try dividing 178,475 by 3:

178,475 ÷ 3 = 59,491.6667

If the quotient is a whole number, then 3 and 59,491.6667 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:

1 178,475
-1 -178,475

Let's try dividing by 4:

178,475 ÷ 4 = 44,618.75

If the quotient is a whole number, then 4 and 44,618.75 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:

1 178,475
-1 178,475
Keep dividing by the next highest number until you cannot divide anymore.

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

15112555591212752956056491,4753,0253,2457,13916,22535,695178,475
-1-5-11-25-55-59-121-275-295-605-649-1,475-3,025-3,245-7,139-16,225-35,695-178,475

More Examples

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