when 20 is divided by a positive integer n, the remainder is 2. how many possible values are there for n?
3,6,9 and 18, since 20/18 also has a remainder of 2.
3, 6, 9
How do you get those answers, could you show a step by step ?
Since there is a remainder of 2 when 20 is divided by n, it means that there would be a remainder of 0 when 18 is divided by n.
So, n is a divisor of 18.
That is, 3,6,9
Okay thank you so much!!!
ouch. nice catch.
PS:
Also, though 2 is a divisor of 18, it's not a possible value of n, since it also divides 20 evenly.
To determine the number of possible values for n, we need to consider the factors of 20.
To find the factors of 20, we need to identify all the positive integers that divide 20 without leaving any remainder. By doing so, we can determine the possible values for n that satisfy the given condition.
The factors of 20 are: 1, 2, 4, 5, 10, and 20.
However, we are specifically interested in the values where dividing 20 by an integer n leaves a remainder of 2.
If we divide 20 by 1, the remainder is 0, not 2.
If we divide 20 by 2, the remainder is 0, not 2.
If we divide 20 by 4, the remainder is 0, not 2.
If we divide 20 by 5, the remainder is 0, not 2.
If we divide 20 by 10, the remainder is 0, not 2.
If we divide 20 by 20, the remainder is 0, not 2.
Therefore, none of the factors of 20 satisfy the given condition.
Hence, there are 0 possible values for n when 20 is divided by a positive integer n, and the remainder is 2.