Bab 2 Faktor & Gandaan (Tingkatan 1)

1. Adakah 5 faktor bagi 70.

Ya

Tidak

There are indeed 5 factors for the number 70. The factors of 70 are 1, 2, 5, 7, and 70 itself.

Explanation

There are indeed 5 factors for the number 70. The factors of 70 are 1, 2, 5, 7, and 70 itself.

2. Adakah 858 gandaan bagi 6?

Ya

Tidak

Ya, 858 adalah gandaan bagi 6. Untuk menentukan apakah suatu angka adalah gandaan bagi angka lain, kita perlu membagi angka tersebut dengan angka lainnya. Jika hasil bagi adalah bilangan bulat, maka angka tersebut adalah gandaan. Dalam kasus ini, jika kita membagi 858 dengan 6, hasilnya adalah 143. Karena hasilnya adalah bilangan bulat, maka 858 adalah gandaan bagi 6.

Explanation

Ya, 858 adalah gandaan bagi 6. Untuk menentukan apakah suatu angka adalah gandaan bagi angka lain, kita perlu membagi angka tersebut dengan angka lainnya. Jika hasil bagi adalah bilangan bulat, maka angka tersebut adalah gandaan. Dalam kasus ini, jika kita membagi 858 dengan 6, hasilnya adalah 143. Karena hasilnya adalah bilangan bulat, maka 858 adalah gandaan bagi 6.

3. Adakah 1 750 gandaan bagi 7?

Ya

Tidak

Yes, 1,750 is a multiple of 7 because when we divide 1,750 by 7, we get a whole number without any remainder. In this case, 1,750 divided by 7 equals 250. Therefore, 1,750 is a multiple of 7.

Explanation

Yes, 1,750 is a multiple of 7 because when we divide 1,750 by 7, we get a whole number without any remainder. In this case, 1,750 divided by 7 equals 250. Therefore, 1,750 is a multiple of 7.

4. Adakah 11 faktor perdana bagi 221.

Ya

Tidak

There are 11 prime factors for the number 221.

Explanation

There are 11 prime factors for the number 221.

5. Sebuah gudang buku berbentuk segi empat tepat berukuran 25 m panjang dan 20 m lebar dibahagikan kepada plot-plot segi empat sama. Cari sisi yang paling lebar, dalam cm, bagi setiap plot segi empat sama itu.

2 m

4 m

5 m

7 m

not-available-via-ai

Explanation

not-available-via-ai

6. Tentukan FSTB bagi 18 dan 54.

6

12

18

54

The given question asks for the FSTB (Faktor Setiap Terkecil Bersama) or the GCF (Greatest Common Factor) of 18 and 54. The FSTB is the largest number that can divide both 18 and 54 without leaving a remainder. To find the FSTB, we can list the factors of both numbers and find the largest number that appears in both lists. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The largest number that appears in both lists is 18, so 18 is the FSTB or GCF of 18 and 54.

Explanation

The given question asks for the FSTB (Faktor Setiap Terkecil Bersama) or the GCF (Greatest Common Factor) of 18 and 54. The FSTB is the largest number that can divide both 18 and 54 without leaving a remainder. To find the FSTB, we can list the factors of both numbers and find the largest number that appears in both lists. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The largest number that appears in both lists is 18, so 18 is the FSTB or GCF of 18 and 54.

7. Antara berikut, yang manakah bukan faktor bagi 56?

2

7

8

9

The number 56 is not divisible by 9. A factor of a number is a whole number that divides evenly into that number. In this case, 2, 7, and 8 are factors of 56 because they divide evenly into it, but 9 does not.

Explanation

The number 56 is not divisible by 9. A factor of a number is a whole number that divides evenly into that number. In this case, 2, 7, and 8 are factors of 56 because they divide evenly into it, but 9 does not.

8. Antara berikut, yang manakah gandaan sepunya bagi 3 dan 5?

21

63

75

85

The number 75 is the product of 3 and 25. Since 25 is the square of 5, 75 can be expressed as 3 multiplied by 5 multiplied by 5. Therefore, 75 is the correct answer as it is the multiple of both 3 and 5.

Explanation

The number 75 is the product of 3 and 25. Since 25 is the square of 5, 75 can be expressed as 3 multiplied by 5 multiplied by 5. Therefore, 75 is the correct answer as it is the multiple of both 3 and 5.

9. Tentukan FSTB bagi 18, 24 dan 30.

3

4

6

12

The given numbers, 18, 24, and 30, have a common factor of 6. FSTB stands for "Faktor Setiap Terasa Bersama" in Indonesian, which translates to "Common Factor" in English. Therefore, the correct answer is 6.

Explanation

The given numbers, 18, 24, and 30, have a common factor of 6. FSTB stands for "Faktor Setiap Terasa Bersama" in Indonesian, which translates to "Common Factor" in English. Therefore, the correct answer is 6.

10. Senaraikan semua faktor perdana bagi 24.

2

3

5

7

11

13

The given answer lists the prime factors of 24, which are 2 and 3. Prime factors are the prime numbers that divide a given number without leaving a remainder. In this case, 2 and 3 are the prime factors of 24 because they are the only prime numbers that can divide 24 evenly.

Explanation

The given answer lists the prime factors of 24, which are 2 and 3. Prime factors are the prime numbers that divide a given number without leaving a remainder. In this case, 2 and 3 are the prime factors of 24 because they are the only prime numbers that can divide 24 evenly.

Submit

11. Apakah faktor sepunya bagi 86 dan 112?

1 dan 2

1 dan 4

2 dan 4

4 dan 12

The factors of 86 are 1 and 86, and the factors of 112 are 1, 2, 4, 8, 14, 16, 28, 56, and 112. However, the question asks for the "common factors" of 86 and 112, which means we need to find the factors that both numbers have in common. The only common factors between 86 and 112 are 1 and 2.

Explanation

The factors of 86 are 1 and 86, and the factors of 112 are 1, 2, 4, 8, 14, 16, 28, 56, and 112. However, the question asks for the "common factors" of 86 and 112, which means we need to find the factors that both numbers have in common. The only common factors between 86 and 112 are 1 and 2.

12. Cari semua faktor bagi 15.

1

2

3

4

5

6

10

15

The given answer lists all the factors of 15. Factors are the numbers that can be multiplied together to get a given number. In this case, 1, 3, 5, and 15 are all numbers that can be multiplied together to get 15.

Explanation

The given answer lists all the factors of 15. Factors are the numbers that can be multiplied together to get a given number. In this case, 1, 3, 5, and 15 are all numbers that can be multiplied together to get 15.

Submit

13. Bakeri Arisa membuat 24 biji mufin coklat, 32 biji mufin vanila dan 48 biji mufin tiramisu. Kesemua mufin itu dimasukkan ke dalam beberapa bungkus plastik untuk dijual di kedai. Setiap bungkusan itu terdiri daripada ketiga-tiga perisa mufin itu dan bilangan muffin bagi setiap jenis adalah sama banyak. Jika setiap bungkusan itu diisi dengan bilangan mufin yang paling banyak, berapakah bilangan bungkusan plastik yang diperlukannya?

4

6

8

12

Bakeri Arisa membuat 24 biji mufin coklat, 32 biji mufin vanila dan 48 biji mufin tiramisu. Jumlah total mufin yang dibuat adalah 24 + 32 + 48 = 104 biji. Setiap bungkusan akan diisi dengan bilangan mufin yang paling banyak, dan bilangan muffin bagi setiap jenis adalah sama banyak. Bilangan muffin yang paling banyak adalah 24, sehingga bilangan bungkusan plastik yang diperlukan adalah 104/24 = 4.33. Karena tidak mungkin memiliki bungkusan plastik sebagian, maka bilangan bungkusan plastik yang diperlukan adalah 4.

Explanation

Bakeri Arisa membuat 24 biji mufin coklat, 32 biji mufin vanila dan 48 biji mufin tiramisu. Jumlah total mufin yang dibuat adalah 24 + 32 + 48 = 104 biji. Setiap bungkusan akan diisi dengan bilangan mufin yang paling banyak, dan bilangan muffin bagi setiap jenis adalah sama banyak. Bilangan muffin yang paling banyak adalah 24, sehingga bilangan bungkusan plastik yang diperlukan adalah 104/24 = 4.33. Karena tidak mungkin memiliki bungkusan plastik sebagian, maka bilangan bungkusan plastik yang diperlukan adalah 4.

14. Aiman menyimpan wang sebanyak RM 1 setiap 8 hari, RM 2 setiap 4 hari dan RM 5 setiap 2 hari. Bilakah dia akan menyimpan duitnya serentak?

Hari ke-3

Hari ke-6

Hari ke-8

Hari ke-10

Aiman akan menyimpan duitnya serentak pada Hari ke-8. Pada Hari ke-3, dia hanya menyimpan RM 1 setiap 8 hari, jadi dia belum mencapai hari ke-8 untuk menyimpan duitnya serentak. Pada Hari ke-6, dia menyimpan RM 2 setiap 4 hari, tetapi ini juga belum mencapai hari ke-8. Pada Hari ke-8, dia akan menyimpan RM 1 dan RM 5, karena ini adalah kelipatan dari kedua interval penyimpanannya. Pada Hari ke-10, meskipun dia akan menyimpan RM 2 dan RM 5, ini bukanlah jawaban yang benar karena pertanyaan meminta kapan dia akan menyimpan duitnya serentak.

Explanation

Aiman akan menyimpan duitnya serentak pada Hari ke-8. Pada Hari ke-3, dia hanya menyimpan RM 1 setiap 8 hari, jadi dia belum mencapai hari ke-8 untuk menyimpan duitnya serentak. Pada Hari ke-6, dia menyimpan RM 2 setiap 4 hari, tetapi ini juga belum mencapai hari ke-8. Pada Hari ke-8, dia akan menyimpan RM 1 dan RM 5, karena ini adalah kelipatan dari kedua interval penyimpanannya. Pada Hari ke-10, meskipun dia akan menyimpan RM 2 dan RM 5, ini bukanlah jawaban yang benar karena pertanyaan meminta kapan dia akan menyimpan duitnya serentak.

15. Tentukan FSTB bagi 12 dan 36.

4

6

12

36

The given numbers are 12 and 36. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The common factor between 12 and 36 is 12. Therefore, the FSTB (Factors Set Terbesar Bersama) or the greatest common factor of 12 and 36 is 12.

Explanation

The given numbers are 12 and 36. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The common factor between 12 and 36 is 12. Therefore, the FSTB (Factors Set Terbesar Bersama) or the greatest common factor of 12 and 36 is 12.

16. Cari semua faktor sepunya bagi : 30 dan 36

1

2

3

4

5

6

8

The given answer lists all the factors of 30 and 36. Factors are the numbers that can be divided evenly into a given number. In this case, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The answer provided only includes the factors that are common to both 30 and 36, which are 1, 2, 3, and 6.

Explanation

The given answer lists all the factors of 30 and 36. Factors are the numbers that can be divided evenly into a given number. In this case, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The answer provided only includes the factors that are common to both 30 and 36, which are 1, 2, 3, and 6.

Submit

17. Padankan setiap yang berikut dengan gandaan yang betul.

6

7

11

13

Submit

18. Cari GSTK bagi 6, 12 dan 24.

6

12

24

32

The given sequence is a list of numbers. The pattern in the sequence is that each number is obtained by adding 6 to the previous number. Starting from 6, each subsequent number is obtained by adding 6 to the previous number. Therefore, the next number in the sequence would be 24.

Explanation

The given sequence is a list of numbers. The pattern in the sequence is that each number is obtained by adding 6 to the previous number. Starting from 6, each subsequent number is obtained by adding 6 to the previous number. Therefore, the next number in the sequence would be 24.

19. Berikut merupakan gandaan bagi 4, kecuali

2

4

8

12

16

18

20

The given sequence consists of multiples of 4, except for the numbers 2 and 18. The numbers 4, 8, 12, 16, and 20 are all multiples of 4 as they can be obtained by multiplying 4 by 1, 2, 3, 4, and 5 respectively. However, the numbers 2 and 18 are not multiples of 4 as they cannot be obtained by multiplying 4 by any whole number. Therefore, the correct answer is 2 and 18.

Explanation

The given sequence consists of multiples of 4, except for the numbers 2 and 18. The numbers 4, 8, 12, 16, and 20 are all multiples of 4 as they can be obtained by multiplying 4 by 1, 2, 3, 4, and 5 respectively. However, the numbers 2 and 18 are not multiples of 4 as they cannot be obtained by multiplying 4 by any whole number. Therefore, the correct answer is 2 and 18.

Submit

20. Cari hasil tambah faktor perdana bagi 96.

5

9

12

16

The number 96 can be factored into 2^5 * 3. When looking for prime factors, we start with the smallest prime number, which is 2. We divide 96 by 2 and get 48. We continue dividing by 2 until we can no longer divide evenly. In this case, we can divide by 2 five times. So, the prime factorization of 96 includes 2 raised to the power of 5. Therefore, the correct answer is 5.

Explanation

The number 96 can be factored into 2^5 * 3. When looking for prime factors, we start with the smallest prime number, which is 2. We divide 96 by 2 and get 48. We continue dividing by 2 until we can no longer divide evenly. In this case, we can divide by 2 five times. So, the prime factorization of 96 includes 2 raised to the power of 5. Therefore, the correct answer is 5.