Q: What are the factor combinations of the number 7,300,315?

 A:
Positive:   1 x 73003155 x 146006311 x 66366523 x 31740529 x 25173555 x 132733115 x 63481145 x 50347199 x 36685253 x 28855319 x 22885667 x 10945995 x 73371265 x 57711595 x 45772189 x 3335
Negative: -1 x -7300315-5 x -1460063-11 x -663665-23 x -317405-29 x -251735-55 x -132733-115 x -63481-145 x -50347-199 x -36685-253 x -28855-319 x -22885-667 x -10945-995 x -7337-1265 x -5771-1595 x -4577-2189 x -3335


How do I find the factor combinations of the number 7,300,315?

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 7,300,315, 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 7,300,315
-1 -7,300,315

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 7,300,315.

Example:
1 x 7,300,315 = 7,300,315
and
-1 x -7,300,315 = 7,300,315
Notice both answers equal 7,300,315

With that explanation out of the way, let's continue. Next, we take the number 7,300,315 and divide it by 2:

7,300,315 ÷ 2 = 3,650,157.5

If the quotient is a whole number, then 2 and 3,650,157.5 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 7,300,315
-1 -7,300,315

Now, we try dividing 7,300,315 by 3:

7,300,315 ÷ 3 = 2,433,438.3333

If the quotient is a whole number, then 3 and 2,433,438.3333 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 7,300,315
-1 -7,300,315

Let's try dividing by 4:

7,300,315 ÷ 4 = 1,825,078.75

If the quotient is a whole number, then 4 and 1,825,078.75 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 7,300,315
-1 7,300,315
Keep dividing by the next highest number until you cannot divide anymore.

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

15112329551151451992533196679951,2651,5952,1893,3354,5775,7717,33710,94522,88528,85536,68550,34763,481132,733251,735317,405663,6651,460,0637,300,315
-1-5-11-23-29-55-115-145-199-253-319-667-995-1,265-1,595-2,189-3,335-4,577-5,771-7,337-10,945-22,885-28,855-36,685-50,347-63,481-132,733-251,735-317,405-663,665-1,460,063-7,300,315

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