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
