Terminology
- Common Divisor 공약수
- Common Multiple 공배수
- Prime Number 소수
- Least[Lowest] Common Multiple 최소 공배수
- Greatest Common Divisor 최대 공약수
- Identity element 항등원
- Inverse element 역원
- Operating rules of real numbers
- Commutative property 교환 법칙
- Associative property 결합 법칙
- Distributive property 분배 법칙
Greatest Common Divisor
The largest positive integer that divides both i and j with no remainder on division
It is also known as the Greatest Common Factor or the Highest Common Factor
두 수가 서로 공통으로 가지고 있는 약수 중 가장 큰 수
Ex) GCD(12, 18)
Divisor of 12: 1, 2, 3, 4, 6, 12
Divisor of 18: 1, 2, 3, 6, 9, 18
➤ GCD(12, 18) = 6
Prime Number
An integer p is a prime number if and only if its only divisors are 1 and p
Identity Element
Pre-Condition
- Closed for certain operations
- Satisfies Commutative property
When the result of operating an arbitrary element a and element e of a set S is a,
we call e is the identity for the operation = a number that allows the result of an operation to be itself
연산을 한 결과가 자기 자신이 되도록 하는 수 = a ∈ S, a ⊙ e = e ⊙ a = a ➤ e (e ∈ S)
- + operation: 0
Ex) 3 + 0 = 3 - × operation: 1
Ex) 7 * 1 = 7
Inverse element
When the result of operating an arbitrary element a and x of a set S becomes the identity e,
x is called the inverse of a for the operation = a number that produces an Identity Element
연산한 결과가 항등원이 되도록 하는 수 = a ∈ S, a ⊙ x = x ⊙ a = e ➤ x (x ∈ S)
Ex)
When the operation △ is defined as a △ b = a + b - 3 for all real numbers,
find the identity and the inverse element of 5 for the operation △
a + e - 3 = a
➤ e = 3 (Identity Element)
The inverse element of 5 is x, the result of which is the identity element 3
5 △ x = x △ 5 = 3
5 + x - 3 = 3
➤ x = 1 (Inverse Element)
Operating rules
- Commutative property: a ⊙ b = b ⊙ a
- Associative property: (a ⊙ b) ⊙ c = a ⊙ (b ⊙ c)
- Distributive property: (a ⊙ b) △ c = (a △ c) ⊙ (b △ c)