mathematics factors (lisa wong)

8/13/2019 Mathematics Factors (Lisa Wong)

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FACTORS


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FACTORS

Common Factor

Prime Number

Highest Common

Factor


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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


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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.


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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


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"Prime Factorization" is finding which

prime numbersmultiply together tomake the original number.


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A composite number can be writtenas a product of all of its prime

factors.

Prime factorization is achieved

when all the factors are primenumbers.


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(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.


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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


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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 .


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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.


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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.


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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


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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


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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


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Find the highest common factor of 14 and 28.

Solution :14 = 1 14 28 = 1 28

= 2 7 = 2 14

= 4 7


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Highest common factor of 14 :2 14

7 7

1Highest common factor of 28 :

7 28

2 4

2 2

1


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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.


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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


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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


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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


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mathematics factors (lisa wong)

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