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What are Prime and Composite Numbers? Video Lecture | Crash Course for CTET Preparation (English) - CTET & State TET
FAQs on What are Prime and Composite Numbers? Video Lecture - Crash Course for CTET Preparation (English) - 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.
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