Is 48 prime or composite?
Understand the Problem
The question is asking whether the number 48 is a prime number or a composite number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a natural number greater than 1 that can be divided by at least one other number besides 1 and itself. To solve this, we need to determine the divisibility of 48.
Answer
composite
Answer for screen readers
The number 48 is a composite number.
Steps to Solve
- Check if the number is greater than 1
Prime numbers and composite numbers are both greater than 1. The number 48 is greater than 1, so we proceed to the next step.
- Test divisibility by smaller prime numbers
We test if 48 is divisible by smaller prime numbers such as 2, 3, 5, 7, etc.
- Test divisibility by 2: A number is divisible by 2 if it is even. Since 48 is even, it is divisible by 2:
$$ \frac{48}{2} = 24 $$
- Test divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 48 is $4 + 8 = 12$, which is divisible by 3.
$$ \frac{48}{3} = 16 $$
Since 48 is divisible by 2 and 3, it has divisors other than 1 and itself.
- Conclusion
Since 48 can be divided by numbers other than 1 and itself (specifically 2 and 3), it is a composite number.
The number 48 is a composite number.
More Information
Composite numbers have more than two positive divisors. This includes all even numbers greater than 2, as they can at least be divided by 2.
Tips
Common mistakes include misidentifying prime numbers due to not testing all smaller prime numbers for divisibility. Ensure to check divisibility by prime numbers smaller than the square root of the number in question.