Q: What are the factor combinations of the number 37,408,415?

 A:
Positive:   1 x 374084155 x 748168311 x 340076517 x 220049555 x 68015385 x 440099187 x 200045935 x 40009
Negative: -1 x -37408415-5 x -7481683-11 x -3400765-17 x -2200495-55 x -680153-85 x -440099-187 x -200045-935 x -40009


How do I find the factor combinations of the number 37,408,415?

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 37,408,415, 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 37,408,415
-1 -37,408,415

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 37,408,415.

Example:
1 x 37,408,415 = 37,408,415
and
-1 x -37,408,415 = 37,408,415
Notice both answers equal 37,408,415

With that explanation out of the way, let's continue. Next, we take the number 37,408,415 and divide it by 2:

37,408,415 ÷ 2 = 18,704,207.5

If the quotient is a whole number, then 2 and 18,704,207.5 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 37,408,415
-1 -37,408,415

Now, we try dividing 37,408,415 by 3:

37,408,415 ÷ 3 = 12,469,471.6667

If the quotient is a whole number, then 3 and 12,469,471.6667 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 37,408,415
-1 -37,408,415

Let's try dividing by 4:

37,408,415 ÷ 4 = 9,352,103.75

If the quotient is a whole number, then 4 and 9,352,103.75 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 37,408,415
-1 37,408,415
Keep dividing by the next highest number until you cannot divide anymore.

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

151117558518793540,009200,045440,099680,1532,200,4953,400,7657,481,68337,408,415
-1-5-11-17-55-85-187-935-40,009-200,045-440,099-680,153-2,200,495-3,400,765-7,481,683-37,408,415

More Examples

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