[Math | Pre Algebra] Fators and multiples

🧭Recall

🧙‍♂️ Factor: divide evenly into another number

🧙‍♂️ Multiple: multiply whole number ‘n’ by another whole number

🧙‍♂️ Prime numbers: divisible by exactly 2 natural numbers (fators are 1 and the number itself)

🧙‍♂️ Composite numbers: have more than 2 way that they can be divided into equal groups

🧙‍♂️ “When there is only one possible way to divide a number into equal sized groups, that number is PRIME”

🧙‍♂️ “Prime Factorization”: break a number untill they got only prime numbers and times of them

🧙‍♂️ “GCD”: Greatest Common divisor (최대공약수)

🧙‍♂️ “LCM”: Least Common Multiple (최소공배수)

📜Note

• Factor: A factor is a whole number that can divide evenly into another number. All numbers have 1 and themselves as factors.

• The factors of 8 are: 1, 2, 4 and 8

• Factor pairs: A factor pair is 2 whole numbers that can be multiplied to get a certain product.

• The factor pairs of 8 are: 1 and 8 because 1 x 8 = 8

• Multiple: A multiple is a number that results when we multiply one whole number by another whole number. The 1st four multiples of 3 are 3, 6, 9 and 12 because:

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    `3 x 1 = 3`
    `3 x 2 = 6`
    `3 x 3 = 9`
    `3 x 4 = 12`

    `15` is a multiple of `3` because `15 / 3 = 5`

• Prime numbers: Natural number, Divisible by exactly 2 natural numbers (1, 2, 3…)
• Composite: Divisible by more than 2 numbers(4, 6, 8, 9 …)
• neither: 1 (only has 1 as a factor = Neither Prime or Composite )

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    ex) `2` is divisible by `1 and 2`(exactly 2 natural numbers), So **2 IS a prime number**
    ex) `3` is also a prime number (divisible by 1 and 3)
    ex) `17` is also a prime number (divisible by 1 and 17) ...

    ex) `4` is divisible by 3 natural numbers (1, 2, 4), So **4 is NOT a prime number**

• Prime factorization

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    Q) What is the prime factorization of 30? = 2(smallest prime number) x 15 = 2 x 3 x 5
    Q) What is the prime factorization of 73? = 73

• Common divisibility examples

• All numbers divisible by 12 & 20 are also divisible by “N”

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    Q)  prime factorization 9 = 3 x 3 
        prime factorization 24 = 2 x 2 x 2 x 3
        prime factorization 9 & 24 = 2 x 2 x 2 x 3 x 3

        N = 9 (3 x 3), 8 (2 x 2 x 2) ... = Common divisibility

• Least common multiple

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    Q)   What is the least common multiple of 18 and 12 
         (Another way to say this is: lcm(18, 12) = ? )
         * lcm = least common multiple

    A)  factorization of 18 = 2 x 9 = 2 x 3 x 3 
        factorization of 12 = 2 x 6 = 2 x 2 x 3

        lcm(18, 12) = 2 x 2 x 3 x 3 = 36

• Greatest common divisor

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    Q)  What is the greatest common divisor of 10 and 7?
        (Another way to say this is: gcd(10, 7) = ? )
        * gcd = greatest common divisor 


    A1)  factors of 10 = 1, 2, 5, 10 
         factors of 7 = 1, 7

         gcd(10, 7) = 1


    A2)  factorization of 10 = 1 x 2 x 5
         factorization of 7 = 1 x 7

         gcd(10, 7) = 1