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Lesson 4 Factor, Prime Factor, GCM, LCM, etc. Factors Definition of factor: 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 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 Note: a common error when listing all factors is to forget 1 and the number itself (1 and 20) Definition(just for knowing) Factoring a number: means to show the number as a product of or more numbers. 36=1x36=6x6=3x12=2x3x6=3x3x4 so on. Prime Number Prime Number is: 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); 2 is only the prime number of all the even numbers. How to determine the prime number? The short path is to use times table to break down the numbers if the numbers only have 1-3 digits. Examples: 24= 121= 325= Continued If the numbers with many digits, you do as the following short cuts : step 1: if the number in Ones column is 0 or 5, the number always can divide by 5 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#) Examples: 2004, 326, 564 Otherwise, divide the number by 3, 5, 7, 11 so on 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 Examples: 35, 105, 600 Examples: 33, 27, 423 Practice: 196 627 1,615 3,330 Prime Factorization Prime factorization of a number means expressing the number as a product of primes; repeating numbers should write as exponent form. Example: 36=2x2x3x3= 2 2 X 32 Greatest Common Factor 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 Example: 36=2x2x3x3 6=2x3 42=2x3x7 18=2x3x3 GCF=2 x3=6 GCF=2x3=6 Tip: GCF is less than or equal to one of the numbers Continued If two numbers or more have no common prime factors. Their GCF is 1 and the numbers are said to be relatively prime. Example: find the GCF of 21 and 55 21=3x7 55=5x11 GCF=1 Least Common Multiple(LCM) Definition: 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 X 1, 2, 3, 4, 5, 6, 7, 8, 9, 6: 6, 12, 18, 24,30,36 15: 15,30,45, 60 Continued LCM 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 1st number, then time the prime numbers of the 2nd number are not include in the 1st #; finally , you compare to the third# so on. FIND LCM of 12, 15, and 18 Practice 12=2x2x3 (write by order from small to large) 15=3x5 18=2x3x3 Lcm=2x2x3x5x3 Find the Lcm of 12, 90, and 105 Note: the LCM always is great than or equal to one of the numbers DO NOW: P81-27,29 (GCF&LCM) 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 2x2x3 2 4 2x2 1 18 2x3x3 3 8 2x2x2 2 16 2x2x2x2 16 35 5x7 35 DO Now P97- 14) 12/15 23) 2/18 57) 108/198 Lesson Summary Complete the follow-up assignment Prepare for next lesson