Q: What are the factor combinations of the number 37,735,691?

 A:
Positive:   1 x 377356917 x 539081319 x 1986089109 x 346199133 x 283727137 x 275443361 x 104531763 x 49457959 x 393492071 x 182212527 x 149332603 x 14497
Negative: -1 x -37735691-7 x -5390813-19 x -1986089-109 x -346199-133 x -283727-137 x -275443-361 x -104531-763 x -49457-959 x -39349-2071 x -18221-2527 x -14933-2603 x -14497


How do I find the factor combinations of the number 37,735,691?

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 37,735,691, 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 37,735,691
-1 -37,735,691

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 37,735,691.

Example:
1 x 37,735,691 = 37,735,691
and
-1 x -37,735,691 = 37,735,691
Notice both answers equal 37,735,691

With that explanation out of the way, let's continue. Next, we take the number 37,735,691 and divide it by 2:

37,735,691 ÷ 2 = 18,867,845.5

If the quotient is a whole number, then 2 and 18,867,845.5 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 37,735,691
-1 -37,735,691

Now, we try dividing 37,735,691 by 3:

37,735,691 ÷ 3 = 12,578,563.6667

If the quotient is a whole number, then 3 and 12,578,563.6667 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 37,735,691
-1 -37,735,691

Let's try dividing by 4:

37,735,691 ÷ 4 = 9,433,922.75

If the quotient is a whole number, then 4 and 9,433,922.75 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 37,735,691
-1 37,735,691
Keep dividing by the next highest number until you cannot divide anymore.

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

17191091331373617639592,0712,5272,60314,49714,93318,22139,34949,457104,531275,443283,727346,1991,986,0895,390,81337,735,691
-1-7-19-109-133-137-361-763-959-2,071-2,527-2,603-14,497-14,933-18,221-39,349-49,457-104,531-275,443-283,727-346,199-1,986,089-5,390,813-37,735,691

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