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Lesson 4

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;

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Lesson 4

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

  2. 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

  3. 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.

  4. 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.

  5. How to determinethe 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=

  6. Continued • If the numbers with many digits, you do as the followingshort 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: 196 627 1,615 3,330

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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 2ndnumber are not include in the 1st #; 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

  12. DO NOW: • P81-27,29 (GCF&LCM) • 27) 18, 22, and 54 • 29) 14, 34, and 60

  13. 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: 122x2x3 2 42x2 1 182x3x3 3 82x2x2 2 162x2x2x2 16 35 5x7 35 • DO Now P97- 14) 12/15 23) 2/18 57) 108/198

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

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