Factors and Divisors of Natural Numbers

Every natural number can be expressed as the product of two natural numbers. Each of these numbers is called a factor of the original number. Factors are also referred to as divisors, as they divide the number without leaving a remainder.

Example: Positive Factors and Divisors of 24

The number 24 can be expressed as different factor pairs:

• 24 = 1 × 24
• 24 = 2 × 12
• 24 = 3 × 8
• 24 = 4 × 6

Positive factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Prime Numbers

Prime numbers are the building blocks of mathematics. Every natural number can be expressed as a product of prime factors, which gives prime numbers special importance. They play a critical role not only in theoretical mathematics but also in modern technology, including cryptography and digital security.

Definition of a Prime Number

A prime number is a natural number greater than 1 that has only two positive divisors: 1 and itself.

Examples :

2, 3, 5, 7, 11, 13, 17, 19, 23, …

Relatively Prime Numbers

Definition: Two numbers are relatively prime if their only common divisor is 1. These numbers do not need to be prime themselves.

Examples:

• 4 and 9 are not prime but are relatively prime.
• 1 is relatively prime to every number.

Twin Primes

Definition: Twin primes are pairs of prime numbers whose difference is 2.

Examples:

• 3 and 5
• 11 and 13
• 17 and 19