Summary: Revision on Natural Numbers and Integers
- The sets of Natural numbers, Whole numbers, Integers and Rational numbers denoted by ℕ, W, ℤ, and ℚ, respectively are described by
- $N= \{1, 2, 3,…\}$
- $W = \{0, 1, 2,…\}$
- $Z= \{…,−3, −2, −1, 0, 1, 2, 3,…\} $
- $Q = \{\frac{a}{b}: a \in ℤ, b \in ℤ, and b\neq 0 \}$
- A composite number is a natural number that has more than two factors.
- The greatest common factor (GCF) of two or more numbers is the greatest factor that is common to all numbers.
- For any numbers a and b, $LCM (a, b) \times GCF (a, b)= a\times b$.
- A prime number is a natural number that has exactly two distinct factors, 1 and itself.
- Prime numbers that differ by two are called twin primes.
- When a natural number is expressed as a product of factors that are all. Prime, then the expression is called the prime factorization of the number.
- Fundamental theorem of arithmetic. – Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.
- The least common multiple (LCM) of two or more numbers is the smallest or least of the common multiples of the numbers.