Q: What are the factor combinations of the number 29,737,673?

 A:
Positive:   1 x 297376737 x 424823929 x 1025437203 x 146491263 x 113071557 x 533891841 x 161533899 x 7627
Negative: -1 x -29737673-7 x -4248239-29 x -1025437-203 x -146491-263 x -113071-557 x -53389-1841 x -16153-3899 x -7627


How do I find the factor combinations of the number 29,737,673?

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 29,737,673, 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 29,737,673
-1 -29,737,673

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 29,737,673.

Example:
1 x 29,737,673 = 29,737,673
and
-1 x -29,737,673 = 29,737,673
Notice both answers equal 29,737,673

With that explanation out of the way, let's continue. Next, we take the number 29,737,673 and divide it by 2:

29,737,673 ÷ 2 = 14,868,836.5

If the quotient is a whole number, then 2 and 14,868,836.5 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 29,737,673
-1 -29,737,673

Now, we try dividing 29,737,673 by 3:

29,737,673 ÷ 3 = 9,912,557.6667

If the quotient is a whole number, then 3 and 9,912,557.6667 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 29,737,673
-1 -29,737,673

Let's try dividing by 4:

29,737,673 ÷ 4 = 7,434,418.25

If the quotient is a whole number, then 4 and 7,434,418.25 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 29,737,673
-1 29,737,673
Keep dividing by the next highest number until you cannot divide anymore.

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

17292032635571,8413,8997,62716,15353,389113,071146,4911,025,4374,248,23929,737,673
-1-7-29-203-263-557-1,841-3,899-7,627-16,153-53,389-113,071-146,491-1,025,437-4,248,239-29,737,673

More Examples

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