Q: What are the factor combinations of the number 7,742,021?

 A:
Positive:   1 x 77420217 x 110600317 x 45541343 x 18004789 x 86989119 x 65059289 x 26789301 x 25721623 x 12427731 x 105911513 x 51172023 x 3827
Negative: -1 x -7742021-7 x -1106003-17 x -455413-43 x -180047-89 x -86989-119 x -65059-289 x -26789-301 x -25721-623 x -12427-731 x -10591-1513 x -5117-2023 x -3827


How do I find the factor combinations of the number 7,742,021?

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 7,742,021, 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 7,742,021
-1 -7,742,021

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 7,742,021.

Example:
1 x 7,742,021 = 7,742,021
and
-1 x -7,742,021 = 7,742,021
Notice both answers equal 7,742,021

With that explanation out of the way, let's continue. Next, we take the number 7,742,021 and divide it by 2:

7,742,021 ÷ 2 = 3,871,010.5

If the quotient is a whole number, then 2 and 3,871,010.5 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 7,742,021
-1 -7,742,021

Now, we try dividing 7,742,021 by 3:

7,742,021 ÷ 3 = 2,580,673.6667

If the quotient is a whole number, then 3 and 2,580,673.6667 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 7,742,021
-1 -7,742,021

Let's try dividing by 4:

7,742,021 ÷ 4 = 1,935,505.25

If the quotient is a whole number, then 4 and 1,935,505.25 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 7,742,021
-1 7,742,021
Keep dividing by the next highest number until you cannot divide anymore.

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

171743891192893016237311,5132,0233,8275,11710,59112,42725,72126,78965,05986,989180,047455,4131,106,0037,742,021
-1-7-17-43-89-119-289-301-623-731-1,513-2,023-3,827-5,117-10,591-12,427-25,721-26,789-65,059-86,989-180,047-455,413-1,106,003-7,742,021

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