Test: Number, Square Numbers - Year 5 MCQ

A prime number has exactly two distinct positive divisors: 1 and itself. The number 17 meets this criterion since its only divisors are 1 and 17. Recognizing prime numbers is crucial in number theory and has applications in cryptography.

The Sieve of Eratosthenes is an ancient algorithm used to identify all prime numbers up to a specified integer. By systematically crossing out the multiples of each prime starting from 2, the remaining numbers are primes. This efficient method highlights how primes can be found without direct division.

A number is divisible by 2 if its ones digit is even, which includes the digits 0, 2, 4, 6, and 8. This simple rule helps quickly determine divisibility without performing long division, making it a handy tool in arithmetic.

A prime number is defined as a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For instance, the number 7 is prime because its only divisors are 1 and 7. Interestingly, the number 2 is the only even prime number, highlighting that all other even numbers can be divided by 2, thus having more than two divisors.

The Sieve of Eratosthenes is an efficient algorithm used to identify all prime numbers up to a given limit, typically 100. It works by iteratively marking the multiples of each prime number starting from 2, thus eliminating non-prime numbers. This method not only highlights the beauty of number theory but also serves as a foundational technique in computational mathematics for generating lists of primes efficiently.