Lesson 4 Factor Prime Factor GCM LCM etc

Lesson 4 Factor, Prime Factor, GCM, LCM, etc.

Factors n Definition of factor: q If a and b are whole numbers, a is said to be a factor of b if a divides b with no remainder. Examples: List all factors of 20 n q q q divide 20 by 1 is equate to 20 ; 1, 20; 20 by 2 =10 ; 2, 10; 20 by 3 have remainder so 3 is not the factor of 20; 20 by 4 = 5; 4, 5; or 20 by 5=4 is repeating ( 4 and 5) ---do not count. The factor of 20 : 1, 20; 2, 10; and 4, 5

Tips n Note: a common error when listing all factors is to forget 1 and the number itself (1 and 20) n Definition (just for knowing) q q Factoring a number: means to show the number as a product of or more numbers. 36=1 x 36=6 x 6=3 x 12=2 x 3 x 6=3 x 3 x 4 so on.

Prime Number n Prime Number is: q q n a whole number has exactly two different factors Note: 1 is not the prime number because it has 1 &1 two factors ( are not different); q 2 is only the prime number of all the even numbers. q

How to determine the prime number? n n The short path is to use times table to break down the numbers if the numbers only have 1 -3 digits. Examples: q q q 24= 121= 325=

Continued n If the numbers with many digits, you do as the following short cuts : n step 1: if the number in Ones column is 0 or 5, the number always can divide by 5 q n step 2: to judge the num# in ones column is even or odd number ( 2, 4, 6, 8, 0 is even / 1, 3, 5, 7, 9 is odd#) q n Examples: 2004, 326, 564 Otherwise, divide the number by 3, 5, 7, 11 so on q n Example: 36’s 6 is even so the number is even number. Step 3: if ones column of the numbers is even number, it can divide by 2 q n Examples: 35, 105, 600 Examples: 33, 27, 423 Practice: 196 627 1, 615 3, 330

Prime Factorization n Prime factorization of a number means expressing the number as a product of primes; repeating numbers should write as exponent form. q Example: n 36=2 x 2 x 3 x 3= X

Greatest Common Factor n Definition: the Greatest Common Factor (GCF) of two or more numbers is the product of all prime factors common to the number. Tip: when you line up the numbers should be by order from small to large q Example: 36=2 x 2 x 3 x 3 6=2 x 3 42=2 x 3 x 7 18=2 x 3 x 3 GCF=2 x 3=6 GCF=2 x 3=6 Tip: GCF is less than or equal to one of the numbers

Continued n If two numbers or more have no common prime factors. Their GCF is 1 and the numbers are said to be relatively prime. q Example: find the GCF of 21 and 55 21=3 x 7 55=5 x 11 GCF=1

Least Common Multiple(LCM) n Definition: q q Multiple of a number A are the numbers obtained by multiplying the number A by the whole numbers 1, 2, 3, 4, …. Example: Find the LCM of 6 and 15 n X 1, 2, 3, 4, 5, 6, 7, 8, 9, n 6: 6, 12, 18, 24, 30, 36 n 15: 15, 30, 45, 60

Continued LCM n n Definition: the LCM of a set of numbers is the smallest numbers that is a multiple of each number in the set. ( short cut) LCM is equal to the product of prime numbers of the 1 st number, then time the prime numbers of the 2 nd number are not include in the 1 st #; finally , you compare to the third# so on. q FIND LCM of 12, 15, and 18 n n q Practice n n 12=2 x 2 x 3 (write by order from small to large) 15=3 x 5 18=2 x 3 x 3 Lcm=2 x 2 x 3 x 5 x 3 Find the Lcm of 12, 90, and 105 Note: the LCM always is great than or equal to one of the numbers

DO NOW: n P 81 -27, 29 (GCF&LCM) q q 27) 18, 22, and 54 29) 14, 34, and 60

REDUCE: Rule to reduce or simplify a fraction, factor both the Numerator and Denominator into primes and the divide out all common factors using the fundamental principle of fractions. • Example: 12 2 x 2 x 3 2 4 2 x 2 1 18 2 x 3 x 3 3 8 2 x 2 x 2 2 16 2 x 2 x 2 x 2 16 35 5 x 7 35 n DO Now P 97 - 14) 12/15 23) 2/18 57) 108/198 •

Lesson Summary n n Complete the follow-up assignment Prepare for next lesson