lesson 4 factor, prime factor, gcm, lcm, etc.. factors definition of factor: if a and b are whole...
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![Page 1: 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](https://reader036.vdocument.in/reader036/viewer/2022082818/56649ec85503460f94bd5c55/html5/thumbnails/1.jpg)
Lesson 4
Factor, Prime Factor, GCM, LCM, etc.
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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
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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.
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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.
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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?
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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: 196 627 1,615 3,330
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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 3222
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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
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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
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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
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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
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
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DO NOW:
P81-27,29 (GCF&LCM) 27) 18, 22, and 54 29) 14, 34, and 60
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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
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Lesson Summary
Complete the follow-up assignment Prepare for next lesson