Question: If a number is divisible by 2 and 3, is it prime?
Options:
Yes
No
Only if it\'s 6
Only if it\'s odd
Correct Answer: No
Solution:
No, because if a number is divisible by 2 and 3, it has divisors other than 1 and itself.
If a number is divisible by 2 and 3, is it prime?
Practice Questions
Q1
If a number is divisible by 2 and 3, is it prime?
Yes
No
Only if it's 6
Only if it's odd
Questions & Step-by-Step Solutions
If a number is divisible by 2 and 3, is it prime?
Step 1: Understand what it means for a number to be divisible by 2 and 3. This means that when you divide the number by 2, there is no remainder, and when you divide it by 3, there is also no remainder.
Step 2: Identify what a prime number is. A prime number is a number greater than 1 that has no divisors other than 1 and itself.
Step 3: If a number is divisible by 2, it means it can be divided by 2 (for example, 4, 6, 8). If it is also divisible by 3, it can be divided by 3 (for example, 6, 12, 18).
Step 4: Check if a number that is divisible by both 2 and 3 can be prime. For example, the number 6 is divisible by both 2 and 3, but it can be divided by 1, 2, 3, and 6. This means it has more divisors than just 1 and itself.
Step 5: Conclude that if a number is divisible by both 2 and 3, it cannot be prime because it has divisors other than 1 and itself.
Divisibility – Understanding the conditions under which a number is divisible by other numbers.
Prime Numbers – A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself.
Composite Numbers – A composite number is a positive integer that has at least one positive divisor other than one or itself.
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