If a number is divisible by 2 and 3, is it prime or composite?

₹0.0

Question: If a number is divisible by 2 and 3, is it prime or composite?

Options:

Correct Answer: Composite

Solution:

A number divisible by 2 and 3 is composite, as it has divisors other than 1 and itself.

If a number is divisible by 2 and 3, is it prime or composite?

If a number is divisible by 2 and 3, is it prime or composite?

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 and by 3, there is no remainder.
Step 2: Identify what a prime number is. A prime number has exactly two distinct positive divisors: 1 and itself.
Step 3: Identify what a composite number is. A composite number has more than two positive divisors.
Step 4: If a number is divisible by both 2 and 3, it must be at least 6 (the smallest number that is divisible by both).
Step 5: Check the divisors of 6. The divisors of 6 are 1, 2, 3, and 6. Since it has more than two divisors, it is composite.
Step 6: Conclude that any number divisible by both 2 and 3 will also have more than two divisors, making it composite.

Divisibility – Understanding the rules of divisibility for numbers, specifically how being divisible by multiple integers affects the classification of a number.
Prime vs Composite – Differentiating between prime numbers (having exactly two distinct positive divisors: 1 and itself) and composite numbers (having more than two positive divisors).