Q is a prime number bigger than 10. What is the smallest positive numb...
3Q is a prime number so it can be divide equally by
3Q, by 1 and by the components 3 and Q. The
smallest number therefore is 3.
View all questions of this test
Q is a prime number bigger than 10. What is the smallest positive numb...
To find the smallest positive number (except 1) that can divide 3Q equally, we need to consider the properties of prime numbers and divisibility rules. Let's break down the problem step by step.
Prime Number Properties:
- A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Q is given as a prime number bigger than 10, so we can assume it is greater than 10 and is not divisible by any number other than 1 and itself.
Divisibility Rules:
- For a number to be divisible by another number, it must have all the prime factors of that number.
Analysis:
- The number 3Q is a multiple of both 3 and Q since it is their product.
- Since Q is a prime number, it has no other prime factors except for 1 and itself. Therefore, 3Q must have at least these two prime factors.
Explanation of the Options:
a) 3Q: This is the number we are trying to divide equally. It cannot be the answer since it is the number itself.
b) Q: This option represents the prime number Q itself. Since Q is a prime number, it cannot be divided equally by any number other than 1 and itself. Therefore, this option is not valid.
c) 3: This option represents the number 3. As explained earlier, the number 3Q is a multiple of both 3 and Q. Since Q is a prime number, it has no prime factors other than 1 and itself. Therefore, the smallest positive number (except 1) that can divide 3Q equally is 3.
d) Q 3: This option represents the product of Q and 3. It is the same as 3Q and cannot be the answer.
e) 2Q: This option represents the product of Q and 2. Since Q is a prime number, it cannot be divided equally by 2. Therefore, this option is not valid.
Conclusion:
The smallest positive number (except 1) that can divide 3Q equally is 3, which corresponds to option (c).