A:
Positive:
1 x 302102 x 151053 x 100705 x 60426 x 503510 x 302115 x 201419 x 159030 x 100738 x 79553 x 57057 x 53095 x 318106 x 285114 x 265159 x 190
Negative:
-1 x -30210-2 x -15105-3 x -10070-5 x -6042-6 x -5035-10 x -3021-15 x -2014-19 x -1590-30 x -1007-38 x -795-53 x -570-57 x -530-95 x -318-106 x -285-114 x -265-159 x -190
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 30,210, it is easier to work with a table - it's called factoring from the outside in.
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 | 30,210 | |
| -1 | -30,210 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 30,210.
Example:
1 x 30,210 = 30,210
and
-1 x -30,210 = 30,210
Notice both answers equal 30,210
With that explanation out of the way, let's continue. Next, we take the number 30,210 and divide it by 2:
30,210 ÷ 2 = 15,105
If the quotient is a whole number, then 2 and 15,105 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 15,105 | 30,210 | |
| -1 | -2 | -15,105 | -30,210 |
Now, we try dividing 30,210 by 3:
30,210 ÷ 3 = 10,070
If the quotient is a whole number, then 3 and 10,070 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!
Here is what our table should look like at this step:
| 1 | 2 | 3 | 10,070 | 15,105 | 30,210 | |
| -1 | -2 | -3 | -10,070 | -15,105 | -30,210 |
Let's try dividing by 4:
30,210 ÷ 4 = 7,552.5
If the quotient is a whole number, then 4 and 7,552.5 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 | 2 | 3 | 10,070 | 15,105 | 30,210 | |
| -1 | -2 | -3 | -10,070 | -15,105 | 30,210 |
If you did it right, you will end up with this table:
| 1 | 2 | 3 | 5 | 6 | 10 | 15 | 19 | 30 | 38 | 53 | 57 | 95 | 106 | 114 | 159 | 190 | 265 | 285 | 318 | 530 | 570 | 795 | 1,007 | 1,590 | 2,014 | 3,021 | 5,035 | 6,042 | 10,070 | 15,105 | 30,210 |
| -1 | -2 | -3 | -5 | -6 | -10 | -15 | -19 | -30 | -38 | -53 | -57 | -95 | -106 | -114 | -159 | -190 | -265 | -285 | -318 | -530 | -570 | -795 | -1,007 | -1,590 | -2,014 | -3,021 | -5,035 | -6,042 | -10,070 | -15,105 | -30,210 |
Here are some more numbers to try:
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