What are Prime and Composite Numbers?

# What are Prime and Composite Numbers? Video Lecture | Mathematics & Pedagogy - CTET & State TET

## Mathematics & Pedagogy

151 videos|108 docs|69 tests

## FAQs on What are Prime and Composite Numbers? Video Lecture - Mathematics & Pedagogy - CTET & State TET

 1. What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, it cannot be divided evenly by any other number except for 1 and itself.
 2. What is a composite number?
A composite number is a natural number greater than 1 that is not prime. It can be divided evenly by at least one positive divisor other than 1 and itself. In simpler terms, a composite number has factors other than just 1 and itself.
 3. Can a number be both prime and composite?
No, a number cannot be both prime and composite. By definition, a prime number has exactly two distinct positive divisors (1 and itself), while a composite number has more than two distinct positive divisors. Therefore, a number can only be classified as either prime or composite.
 4. How can I determine if a number is prime or composite?
To determine if a number is prime or composite, you can check its divisors. Start by dividing the number by 2 and continue dividing it by subsequent natural numbers up to its square root. If at any point the number is evenly divisible, then it is a composite number. However, if no divisors are found, the number is prime.
 5. Are there infinitely many prime numbers?
Yes, there are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid over 2,000 years ago. Euclid's proof shows that if you have a list of prime numbers, you can always find a larger prime number by multiplying all the primes together and adding 1. Therefore, prime numbers continue indefinitely.

## Mathematics & Pedagogy

151 videos|108 docs|69 tests

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