Bathroom Tiling

Make possible ways to arrange the tiles.

1. Use 4 tiles

2. Use 6 tiles

3. Use 3 tiles

4. Use 5 tiles

For 4 tiles and 6 tiles

the factors are more than two:

4 tiles – factors are 4, 2 and 1

6 tiles – factors are 6, 3 and 1

Numbers with more than 2 factors are called

For 3 tiles and 5 tiles

the factors are ONLY two:

3 tiles – factors are 3 and 1

5 tiles – factors are 5 and 1

Numbers with ONLY two factors are called

Sieve of Eratosthenes1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

48 64 22 85 39 2 42 14 12

74 63 56 21 15 17 70 57 42

20 63 16 18 62 59 83 37 22

12 42 84 42 60 39 21 31 53

30 43 43 13 60 15 72 46 11

62 31 72 53 29 13 13 2 41

17 73 22 86 8 12 28 25 66

3 80 38 71 11 3 73 42 81

61 26 42 7 12 50 61 8 33

11 83 83 7 57 19 5 38 25

74 60 84 30 22 43 80 49 55

Assessment: Write C if the number is composite and P if it is prime.

1. 67 ___

2. 100 ___

3. 81 ___

4. 43 ___

5. 31 ___

 

Write true or false.

1. The least prime number is 3.

2. The product of two prime numbers is a prime number.

3. All even numbers greater than 2 are composite.

4. The sum of any two prime numbers is a composite number.

5. The only even prime number is 2.

HomeworkA. Answer the following questions: (1/2 sheet of paper, crosswise)

1. I am a three-digit number. I am the sum of the prime numbers between 40 and 60. Who am I?

2. What is the sum of the first prime numbers?

3. List the twin primes between 1 to 100.

4. Name two composite numbers that are prime.

5. Name three consecutive odd prime numbers.

6. Which is the smallest prime number?

7. How many prime numbers are there between 1 and 100?

8. Is every odd number other than 1 a prime number?

9. Is every even number other than 2 a composite number?

10. What are the first 10 prime numbers?

See you all tomorrow!

Prepared by:

DEMOSTHENES O. CAJES

Teacher I, DCCES

Sieve of Eratosthenes

Eratosthenes (276-194 B.C.) was the third librarian of the famous library in Alexandria and an outstanding scholar all around. He is remembered by his measurement of the circumference of the Earth, estimates of the distances to the sun and the moon, and, in mathematics, for the invention of an algorithm for collecting prime numbers. The algorithm is known as the Sieve of Eratosthenes.

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