Q: What are the factor combinations of the number 3,421,733?

 A:
Positive:   1 x 34217337 x 48881923 x 14877153 x 64561161 x 21253371 x 9223401 x 85331219 x 2807
Negative: -1 x -3421733-7 x -488819-23 x -148771-53 x -64561-161 x -21253-371 x -9223-401 x -8533-1219 x -2807


How do I find the factor combinations of the number 3,421,733?

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 3,421,733, 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 3,421,733
-1 -3,421,733

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 3,421,733.

Example:
1 x 3,421,733 = 3,421,733
and
-1 x -3,421,733 = 3,421,733
Notice both answers equal 3,421,733

With that explanation out of the way, let's continue. Next, we take the number 3,421,733 and divide it by 2:

3,421,733 ÷ 2 = 1,710,866.5

If the quotient is a whole number, then 2 and 1,710,866.5 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 3,421,733
-1 -3,421,733

Now, we try dividing 3,421,733 by 3:

3,421,733 ÷ 3 = 1,140,577.6667

If the quotient is a whole number, then 3 and 1,140,577.6667 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 3,421,733
-1 -3,421,733

Let's try dividing by 4:

3,421,733 ÷ 4 = 855,433.25

If the quotient is a whole number, then 4 and 855,433.25 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 3,421,733
-1 3,421,733
Keep dividing by the next highest number until you cannot divide anymore.

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

1723531613714011,2192,8078,5339,22321,25364,561148,771488,8193,421,733
-1-7-23-53-161-371-401-1,219-2,807-8,533-9,223-21,253-64,561-148,771-488,819-3,421,733

More Examples

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