mathematics factors (lisa wong)
Post on 04-Jun-2018
229 Views
Preview:
TRANSCRIPT
-
8/13/2019 Mathematics Factors (Lisa Wong)
1/25
FACTORS
-
8/13/2019 Mathematics Factors (Lisa Wong)
2/25
-
8/13/2019 Mathematics Factors (Lisa Wong)
3/25
-
8/13/2019 Mathematics Factors (Lisa Wong)
4/25
FACTORS
Common Factor
Prime Number
Highest Common
Factor
-
8/13/2019 Mathematics Factors (Lisa Wong)
5/25
Factoringis like taking a number apart. It
means to express a number as the product of
its factors.
Factors are either composite numbersor
prime numbers(except that 0 and 1 are
neither prime nor composite).
3 x 4 = 12
3 and 4 are both factors of 12
12 is a multiple of both 3 and 4.
The number 12 is a multipleof 3, because it can
be divided evenly by 3.
http://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.htmlhttp://www.math.com/school/subject1/lessons/S1U3L1GL.html -
8/13/2019 Mathematics Factors (Lisa Wong)
6/25
List all the factors of 42.
42 = 142
= 221
= 314= 67
So, the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Note:
425=8This shows that 5 does not divide exactly into 42 .
So, 5 is not a factor of 42.
-
8/13/2019 Mathematics Factors (Lisa Wong)
7/25
A Prime Numbercan be dividedevenly onlyby 1 or itself and it must
be a whole number greater than 1.
http://www.mathsisfun.com/prime-composite-number.htmlhttp://www.mathsisfun.com/prime-composite-number.html -
8/13/2019 Mathematics Factors (Lisa Wong)
8/25
-
8/13/2019 Mathematics Factors (Lisa Wong)
9/25
"Prime Factorization" is finding which
prime numbersmultiply together tomake the original number.
-
8/13/2019 Mathematics Factors (Lisa Wong)
10/25
A composite number can be writtenas a product of all of its prime
factors.
Prime factorization is achieved
when all the factors are primenumbers.
-
8/13/2019 Mathematics Factors (Lisa Wong)
11/25
(A)2 2 3 = 12
(B)2 3 7 = 42
(C) 2 2 3 7 11 = 924
2 3 10 = 60The reason is that 10 isnot a prime number.
-
8/13/2019 Mathematics Factors (Lisa Wong)
12/25
http://www.mathsteacher.com.au/year7/ch03_prime/04_factor/fac.htmhttp://www.mathsteacher.com.au/year7/ch03_prime/04_factor/fac.htmhttp://www.mathsteacher.com.au/year7/ch03_prime/04_factor/fac.htmhttp://www.mathsteacher.com.au/year7/ch03_prime/04_factor/fac.htm -
8/13/2019 Mathematics Factors (Lisa Wong)
13/25
What are the prime factors of 90 ?
Solution :
5 90
3 18
3 6
2 0
So the prime factors of 90 are 3, 3, 2 and 5 .
-
8/13/2019 Mathematics Factors (Lisa Wong)
14/25
Find the common factors of 10 and 30.
Solution :
10 = 1 10 30 = 1 30= 2 5 = 2 15
= 5 6
= 3 10
So, the common factors of 10 and 30 are 1, 2,
5 and 10.
-
8/13/2019 Mathematics Factors (Lisa Wong)
15/25
Find the common factors of 26 and 39.
Solution:
26 = 1 26 39 = 1 39
= 2 13 = 3 13
Since 26 and 39 have same number after divide thatis 1 and 13.
So, the common factors of 26 and 39 are 1 and 13.
-
8/13/2019 Mathematics Factors (Lisa Wong)
16/25
What are the common factors of 15, 30 and
105?
Factor of 15: Factor of 30: Factor of 105:
15 = 3 5 30 = 1 30 105 = 1 105
= 1 15 = 2 15 = 3 35
= 3 10 = 5 21= 5 6 = 7 15
-
8/13/2019 Mathematics Factors (Lisa Wong)
17/25
The factors that are common to all three
numbers are 1, 3, 5and 15
In other words, the common factorsof 15, 30
and 105 are 1, 3, 5and 15
-
8/13/2019 Mathematics Factors (Lisa Wong)
18/25
The largest common factorof two or morenumbers is called the highest common factor(HCF).
In general:
To find the highest common factorof two (ormore) numbers, make prime factorsof thenumbers and identify the common primefactors. Then the highest common factor is theproductof the common prime factors.
http://www.mathsteacher.com.au/year7/ch03_prime/05_comm/fac.htmhttp://www.mathsteacher.com.au/year8/ch04_algebra/12_hcf/hcf.htmhttp://www.mathsteacher.com.au/year8/ch01_arithmetic/05_prime/numb.htmhttp://www.mathsteacher.com.au/year8/ch01_arithmetic/01_basic/oper.htmhttp://www.mathsteacher.com.au/year8/ch01_arithmetic/01_basic/oper.htmhttp://www.mathsteacher.com.au/year8/ch01_arithmetic/05_prime/numb.htmhttp://www.mathsteacher.com.au/year8/ch04_algebra/12_hcf/hcf.htmhttp://www.mathsteacher.com.au/year7/ch03_prime/05_comm/fac.htm -
8/13/2019 Mathematics Factors (Lisa Wong)
19/25
Find the highest common factor of 14 and 28.
Solution :14 = 1 14 28 = 1 28
= 2 7 = 2 14
= 4 7
-
8/13/2019 Mathematics Factors (Lisa Wong)
20/25
Highest common factor of 14 :2 14
7 7
1Highest common factor of 28 :
7 28
2 4
2 2
1
-
8/13/2019 Mathematics Factors (Lisa Wong)
21/25
Since 14 and 28 have the same common factor
that is, 7 and 2 .
So, the highest common factor of 14 and 28 is
7 2 = 14.
-
8/13/2019 Mathematics Factors (Lisa Wong)
22/25
Find the highest common factor of 60 and 150.
Solution:
The prime factorisation of 60 is :
2 2 3 5 = 2 3 5
Therefore , 60 = 2 30
= 2 2 15
= 2 2 3 5
-
8/13/2019 Mathematics Factors (Lisa Wong)
23/25
The prime factorisation of 150 is :
2 3 5 5 = 2 3 5
Therefore , 150 = 2 75
= 2 3 25
= 2 3 5 5Product of common prime
factor
So, the highest common factor (HCF) = 2 3 5
= 30
-
8/13/2019 Mathematics Factors (Lisa Wong)
24/25
The highest common factorcan also beobtained by a trial and error method.
For example, the highest common factor of40 and 45 is 5 because 5 is the largest number
which divides into both 40 and 45 exactly.
Similarly, the highest common factor of 27
and 36 is 9 because 9 is the largest number
which divides into both 27 and 36 exactly.
http://www.mathsteacher.com.au/year8/ch04_algebra/12_hcf/hcf.htmhttp://www.mathsteacher.com.au/year8/ch04_algebra/12_hcf/hcf.htm -
8/13/2019 Mathematics Factors (Lisa Wong)
25/25
THE END
top related