Understanding prime and composite numbers is essential for competitive exams. Here are some tricks to identify them quickly:
1. Prime Numbers
A prime number is a number greater than 1 that has no divisors other than 1 and itself.
- Tip: A prime number has exactly two factors.
- All prime numbers except 2 and 3 follow the pattern
6n ± 1, wherenis a natural number. - Quickly eliminate numbers ending in an even digit (except 2) or 5 (except 5).
- Use divisibility rules to check divisibility by small primes (2, 3, 5, 7, etc.) for larger numbers.
Shortcut: For numbers below 100, memorize the list of prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
2. Composite Numbers
A composite number is a number greater than 1 that is not prime (i.e., it has more than two factors).
- All even numbers greater than 2 are composite.
- If the sum of the digits of a number is divisible by 3, the number is composite (except 3).
- If a number ends with a 0 or 5, it is composite (except 5).
3. Tricks for Quick Identification
- Elimination Method: For a range of numbers, eliminate multiples of known primes to identify remaining primes.
- Sieve of Eratosthenes: Use this ancient algorithm for numbers within a certain range.
- Factorization: Break the number into prime factors. If more than two factors exist, it is composite.
Practice: Regular practice with number ranges and divisibility tests will improve your speed and accuracy.
Example:
- Prime: Check if 47 is divisible by 2, 3, 5, or 7. Since it isn’t, it’s prime.
- Composite: Check if 48 is divisible by 2 (yes). Thus, it’s composite.