Q: What are the factor combinations of the number 427,735?

 A:
Positive:   1 x 4277355 x 855477 x 6110511 x 3888535 x 1222155 x 777777 x 5555101 x 4235121 x 3535385 x 1111505 x 847605 x 707
Negative: -1 x -427735-5 x -85547-7 x -61105-11 x -38885-35 x -12221-55 x -7777-77 x -5555-101 x -4235-121 x -3535-385 x -1111-505 x -847-605 x -707


How do I find the factor combinations of the number 427,735?

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 427,735, 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.

1 427,735
-1 -427,735

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 427,735.

Example:
1 x 427,735 = 427,735
and
-1 x -427,735 = 427,735
Notice both answers equal 427,735

With that explanation out of the way, let's continue. Next, we take the number 427,735 and divide it by 2:

427,735 ÷ 2 = 213,867.5

If the quotient is a whole number, then 2 and 213,867.5 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:

1 427,735
-1 -427,735

Now, we try dividing 427,735 by 3:

427,735 ÷ 3 = 142,578.3333

If the quotient is a whole number, then 3 and 142,578.3333 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:

1 427,735
-1 -427,735

Let's try dividing by 4:

427,735 ÷ 4 = 106,933.75

If the quotient is a whole number, then 4 and 106,933.75 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:

1 427,735
-1 427,735
Keep dividing by the next highest number until you cannot divide anymore.

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

157113555771011213855056057078471,1113,5354,2355,5557,77712,22138,88561,10585,547427,735
-1-5-7-11-35-55-77-101-121-385-505-605-707-847-1,111-3,535-4,235-5,555-7,777-12,221-38,885-61,105-85,547-427,735

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