Q: What are the factor combinations of the number 10,142,023?

 A:
Positive:   1 x 1014202343 x 235861163 x 622211447 x 7009
Negative: -1 x -10142023-43 x -235861-163 x -62221-1447 x -7009


How do I find the factor combinations of the number 10,142,023?

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 10,142,023, 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 10,142,023
-1 -10,142,023

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 10,142,023.

Example:
1 x 10,142,023 = 10,142,023
and
-1 x -10,142,023 = 10,142,023
Notice both answers equal 10,142,023

With that explanation out of the way, let's continue. Next, we take the number 10,142,023 and divide it by 2:

10,142,023 ÷ 2 = 5,071,011.5

If the quotient is a whole number, then 2 and 5,071,011.5 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 10,142,023
-1 -10,142,023

Now, we try dividing 10,142,023 by 3:

10,142,023 ÷ 3 = 3,380,674.3333

If the quotient is a whole number, then 3 and 3,380,674.3333 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 10,142,023
-1 -10,142,023

Let's try dividing by 4:

10,142,023 ÷ 4 = 2,535,505.75

If the quotient is a whole number, then 4 and 2,535,505.75 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 10,142,023
-1 10,142,023
Keep dividing by the next highest number until you cannot divide anymore.

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

1431631,4477,00962,221235,86110,142,023
-1-43-163-1,447-7,009-62,221-235,861-10,142,023

More Examples

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