4-keterbahagian.ppt

7/28/2019 4-keterbahagian.ppt

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Primes and Multiples

2-1 Divisibility Tests2-2 Multiples

2-3 Divisors, Factors, and Greatest Common

Factor (GCF)

2-4 Primes and Composites

2-5 Prime Factorization2-6 Least Common Multiple (LCM )

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2-1 Test for Divisibility of a Natural Number by

2, 3, or 5

1) Divisibility by 2: If the ones place digit iseven ( 0, 2, 4, 6, 8 ), then the number is divisible by 2.

2) Divisibility by 3: If the sum of the digits isdivisible by 3, then the number is divisible by 3.

3) Divisibility by 5: If the ones place digit is 0

or 5, then the number is divisible by 5.

Number Criteria Answer

The one's place digit is 0 which is even 390 is divis ible by 2

sum of digits: 3 + 9 + 0 = 12/3 =4 390 is divis ible by 3

The one's place digit is 0 or 5 390 is divis ible by 5

Is 390 divis ible by 2, 3, or 5 ?

390


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2-1 Test for Divisibility of a Natural Number by

6, 9, or 10

1) Divisibility by 6: If the number is divisibleby 2 and 3, then the number is divisible by 6.

2) Divisibility by 9: If the sum of the digits isdivisible by 9, then the number is divisible by 9.

3) Divisibility by 10: If the ones place digit is

0, then the number is divisible by 10.

Number Criteria Answer

sum of digits: 3 + 9 + 0 = 12/9 390 is not divisible by 9

The one's place digit is 0 390 is divisible by 10

Is 390 divis ible by 6, 9, or 10 ?

390

The one's place digit is 0 which is even

and the sum of digits: 3 + 9 + 0 = 12/3

390 is divis ible by 2

and 3 and 6


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2-2 List the Multiples of a whole number

Multiply the natural number by the

given specified values.

Problem Strategy Answer

5 x 9 = 4523 x 9 = 207

28 x 9 = 252

452 x 9 = 4,068

Finding specific multiples of 9

List the 5th, 23rd,

28th, and 452 nd

multiples of 9


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2-2 Determine whether one whole number

is a multiple of another whole number

If the number is divisible with no remainder (no decimal),

then the natural number is divisible by the specified

number.

Problem Strategy Answer

Is 711 divis ible by 9? 711 / 9 = 79 YesIs 4132 a multiple of 6? 4132 / 6 = 688.666 No

Is 481 a multiple of 13? 481 / 13 = 37 Yes

Is 10 a multiple of 70? 10 / 70 = 0.1428 No

Finding whether a specific number is a multiple of another number


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2-3 Factors

List all the factors (divisors) of a counting number:

1) List all the pairs of factors of the number.

2) Read down the left column and up the right column.

Problem

1 x 150

2 x 75

3 x 50

5 x 30

6 x 25

10 x 15

LIST ALL THE FACTORS OF 150

150

Strategy

Answer = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150


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2-5 Prime Factorization of a counting number

1) The prime factorization is the product of the prime divisors.

Strategy Prime Number Divisors Quotient

2 60

2 303 15

5 5

1

FIND THE PRIME FACTORIZATION OF 60

Divide by prime numbers until the

quotient is 1

Answer = 2 x 2 x 3 x 5 = 22

x 3 x 5


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2-5 Greatest Common Factor (GCF)

Strategy

Prime

Number

Divisors Quotient

Prime

Number

Divisors Quotient

2 66 2 88

3 33 2 44

11 11 2 22

1 11 11

1

Find the GCF of 66 and 88

Write the numbers in prime

factorization form and identify

the common prime factors.

Multiply the common prime

factors.

Answer = 2 x 11 = 22


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2-5 Greatest Common Factor (GCF)

1) Write each number in prime factorization form and identify

the common prime factors.

2) Find the product of the common prime factors.

FIND THE GCF of 80, 100 and 280

Prime

umberivisors uotie

Prime

NumberDivisors uotie

Prime

NumberDivisors Quotient

2 80 2 100 2 280

2 40 2 50 2 140

2 20 5 25 2 70

2 10 5 5 5 35

5 5 1 7 7

1 1

Answer = 22 x 5 = 20


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2-6 Least Common Multiple (LCM)

Strategy

PrimeNumber

Divisors Quotient Quotient Quotient

2 10 15 18

3 5 15 9

5 5 5 3

1 1 3

Answer = 2 x 3 x 5 x 1 x 1 x 3 = 90

Find the LCM 10, 15, and 18 using the Group Prime-Factoring Method

Divide at least two of the

numbers by any common prime

number. Continue until no two

quotients have a commondivisor. Write the product of the

divis ors and the remaining


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HOMEWORK

Q: What is the rule to test whether the number

is divisible by

(a) 4

(b) 7

(c) 8


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(b) Divisibility by 7:

Digit yang terakhir, DIGANDADUAkan.

Tolak nombor baru itu daripada digit-digit yang

lain.

Jika jwpn adalah 0 atau boleh dibahagi dengan

7, maka nombor itu boleh itu dibahagi oleh 7.

679 9 + 9 = 18 DIGIT lain : 67

6718 = 49

49 7 = 7

maka, 679 boleh dibahagi dengan 7.


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(b) Divisibility by 8 ?

/

Boleh dibahagi dengan 8 ?


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(b) Divisibility by 8:

3 Digit terakhir boleh dibahagi dengan8.

3 digit terakhir bagi 10 272 adalah 272

272 8 = 34

maka, 10272 boleh dibahagi dengan 8.

4-keterbahagian.ppt

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