Q: What are the factor combinations of the number 3,674,671?

 A:
Positive:   1 x 36746717 x 52495311 x 33406113 x 28266777 x 4772391 x 40381143 x 256971001 x 3671
Negative: -1 x -3674671-7 x -524953-11 x -334061-13 x -282667-77 x -47723-91 x -40381-143 x -25697-1001 x -3671


How do I find the factor combinations of the number 3,674,671?

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 3,674,671, 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 3,674,671
-1 -3,674,671

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 3,674,671.

Example:
1 x 3,674,671 = 3,674,671
and
-1 x -3,674,671 = 3,674,671
Notice both answers equal 3,674,671

With that explanation out of the way, let's continue. Next, we take the number 3,674,671 and divide it by 2:

3,674,671 ÷ 2 = 1,837,335.5

If the quotient is a whole number, then 2 and 1,837,335.5 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 3,674,671
-1 -3,674,671

Now, we try dividing 3,674,671 by 3:

3,674,671 ÷ 3 = 1,224,890.3333

If the quotient is a whole number, then 3 and 1,224,890.3333 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 3,674,671
-1 -3,674,671

Let's try dividing by 4:

3,674,671 ÷ 4 = 918,667.75

If the quotient is a whole number, then 4 and 918,667.75 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 3,674,671
-1 3,674,671
Keep dividing by the next highest number until you cannot divide anymore.

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

17111377911431,0013,67125,69740,38147,723282,667334,061524,9533,674,671
-1-7-11-13-77-91-143-1,001-3,671-25,697-40,381-47,723-282,667-334,061-524,953-3,674,671

More Examples

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