Transcript Lesson 4

Lesson 4
Factor, Prime Factor, GCM, LCM, etc.
Factors
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Definition of factor:
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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
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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
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Note: a common error when listing all
factors is to forget 1 and the number
itself (1 and 20)
Definition(just for knowing)
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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
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Prime Number is:
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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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How to determine the prime
number?
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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:
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24=
121=
325=
Continued
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If the numbers with many digits, you do as the
following short cuts :
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step 1: if the number in Ones column is 0 or 5, the number
always can divide by 5
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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#)
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Examples: 2004, 326, 564
Otherwise, divide the number by 3, 5, 7, 11 so on
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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
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Examples: 35, 105, 600
Examples: 33, 27, 423
Practice: 196 627 1,615 3,330
Prime Factorization
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Prime factorization of a number means expressing the
number as a product of primes; repeating numbers
should write as exponent form.
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Example:
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36=2x2x3x3= 2 2 X 32
Greatest Common Factor
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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
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If two numbers or more have no common
prime factors. Their GCF is 1 and the
numbers are said to be relatively prime.
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Example: find the GCF of 21 and 55
21=3x7
55=5x11
GCF=1
Least Common Multiple(LCM)
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Definition:
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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
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1, 2, 3, 4, 5, 6, 7, 8, 9,
 6: 6, 12, 18, 24,30,36
 15: 15,30,45, 60
Continued LCM
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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
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Practice
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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:
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P81-27,29 (GCF&LCM)
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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
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Lesson Summary
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Complete the follow-up assignment
Prepare for next lesson