Q: What are the factor combinations of the number 37,474,409?

 A:
Positive:   1 x 374744097 x 535348717 x 220437729 x 1292221119 x 314911203 x 184603493 x 760133451 x 10859
Negative: -1 x -37474409-7 x -5353487-17 x -2204377-29 x -1292221-119 x -314911-203 x -184603-493 x -76013-3451 x -10859


How do I find the factor combinations of the number 37,474,409?

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 37,474,409, 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 37,474,409
-1 -37,474,409

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 37,474,409.

Example:
1 x 37,474,409 = 37,474,409
and
-1 x -37,474,409 = 37,474,409
Notice both answers equal 37,474,409

With that explanation out of the way, let's continue. Next, we take the number 37,474,409 and divide it by 2:

37,474,409 ÷ 2 = 18,737,204.5

If the quotient is a whole number, then 2 and 18,737,204.5 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 37,474,409
-1 -37,474,409

Now, we try dividing 37,474,409 by 3:

37,474,409 ÷ 3 = 12,491,469.6667

If the quotient is a whole number, then 3 and 12,491,469.6667 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 37,474,409
-1 -37,474,409

Let's try dividing by 4:

37,474,409 ÷ 4 = 9,368,602.25

If the quotient is a whole number, then 4 and 9,368,602.25 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 37,474,409
-1 37,474,409
Keep dividing by the next highest number until you cannot divide anymore.

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

1717291192034933,45110,85976,013184,603314,9111,292,2212,204,3775,353,48737,474,409
-1-7-17-29-119-203-493-3,451-10,859-76,013-184,603-314,911-1,292,221-2,204,377-5,353,487-37,474,409

More Examples

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