Q: What are the factor combinations of the number 10,742,333?

 A:
Positive:   1 x 107423337 x 1534619239 x 449471673 x 6421
Negative: -1 x -10742333-7 x -1534619-239 x -44947-1673 x -6421


How do I find the factor combinations of the number 10,742,333?

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 10,742,333, 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 10,742,333
-1 -10,742,333

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 10,742,333.

Example:
1 x 10,742,333 = 10,742,333
and
-1 x -10,742,333 = 10,742,333
Notice both answers equal 10,742,333

With that explanation out of the way, let's continue. Next, we take the number 10,742,333 and divide it by 2:

10,742,333 ÷ 2 = 5,371,166.5

If the quotient is a whole number, then 2 and 5,371,166.5 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 10,742,333
-1 -10,742,333

Now, we try dividing 10,742,333 by 3:

10,742,333 ÷ 3 = 3,580,777.6667

If the quotient is a whole number, then 3 and 3,580,777.6667 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 10,742,333
-1 -10,742,333

Let's try dividing by 4:

10,742,333 ÷ 4 = 2,685,583.25

If the quotient is a whole number, then 4 and 2,685,583.25 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 10,742,333
-1 10,742,333
Keep dividing by the next highest number until you cannot divide anymore.

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

172391,6736,42144,9471,534,61910,742,333
-1-7-239-1,673-6,421-44,947-1,534,619-10,742,333

More Examples

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