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.

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= How to determine the prime number?

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  Examples: 35, 105, 600 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#)  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: 2004, 326, 564 Otherwise, divide the number by 3, 5, 7, 11 so on  Examples: 33, 27, 423 Practice: ,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= X

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 2 nd number are not include in the 1 st #; finally, you compare to the third# so on.  FIND LCM of 12, 15, and 18 12=2x2x3 (write by order from small to large) 15=3x5 18=2x3x3 Lcm=2x2x3x5x3  Practice 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 2x2x x x3x x2x x2x2x x7 35 DO Now P97- 14) 12/15 23) 2/18 57) 108/198

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