# HCF MCQs With Explanation-Sainik School Class 6 Math Study Material Notes free pdf download

**Sainik School Entrance Exam for Class 6 Math Study Material Notes** helps students face the competition in the current education system. In this case, the ANAND CLASSES is the best study tool to get a clear idea about the basics and gain a strong knowledge of the Sainik School Entrance Exam syllabus.

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**Important Multiple-choice questions (MCQs) for Sainik School Entrance Exam related to the HCF (Highest Common Factor)** of numbers, along with explanations for each one discuss as follows **:**

## HCF MCQs |

**Question 1:** What is the HCF of 12 and 18?

## (A) 1 (B) 2 (C) 3 (D) 6

**Answer:** (D)

**Explanation:** The HCF of two numbers is the largest number that is a factor of both numbers. The prime factorization of 12 is 2 * 2 * 3, and the prime factorization of 18 is 2 * 3 * 2. The HCF of 12 and 18 is therefore 2 * 3 = 6.

**Question 2:** What is the HCF of 36, 48, and 60?

## (A) 4 (B) 6 (C) 12 (D) 24

**Answer:** (B)

**Explanation:** The HCF of three or more numbers is the largest number that is a factor of all of the numbers. We can find the HCF of 36, 48, and 60 by first finding the HCF of two of the numbers, and then finding the HCF of that result and the third number.

The HCF of 36 and 48 is 12. The HCF of 12 and 60 is 6.

Therefore, the HCF of 36, 48, and 60 is 6.

**Question 3:** The product of two numbers is 1521 and their HCF is 13. What is the sum of the two numbers?

## (A) 117 (B) 121 (C) 125 (D) 130

**Answer:** (D)

**Explanation:** Let the two numbers be 13a and 13b, where a and b are coprime (have no common factors other than 1). We know that the product of the two numbers is 1521 and their HCF is 13, so:

```
13a * 13b = 1521
ab = 9
```

The only possible values for a and b that satisfy this equation are a = 1 and b = 9, or a = 9 and b = 1. Therefore, the two numbers are 13 and 117, or 117 and 13. The sum of these two numbers is 130.

**Question 4:** The HCF of two numbers is 15 and their LCM is 120. What is the product of the two numbers?

## (A) 1800 (B) 3600 (C) 7200 (D) None of the above

**Answer:** (A)

**Explanation:** We know that the product of two numbers is equal to their HCF times their LCM. Therefore, the product of the two numbers is 15 * 120 = 1800.

**Question 5:** A rectangular field with dimensions 30 m by 48 m is to be divided into the largest possible square plots of equal size. What is the side of each square plot?

## (A) 6 m (B) 12 m (C) 18 m (D) 24 m

**Answer:** (A)

**Explanation:** The side of each square plot must be a common factor of both 30 m and 48 m. The largest common factor of 30 m and 48 m is 6 m. Therefore, the side of each square plot is 6 m.

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**Question 6:** The HCF of two numbers is 1 and their LCM is 120. What are the two numbers?

## (A) 1 and 120 (B) 2 and 60 (C) 3 and 40 (D) 4 and 30

**Answer:** (D)

**Explanation:** We know that the product of two numbers is equal to their HCF times their LCM. Therefore, the product of the two numbers is 1 * 120 = 120. The two factors of 120 that have a HCF of 1 are 4 and 30.

**Question 7:** A train can travel 180 km in 6 hours, while another train can travel 240 km in 8 hours. What is the greatest common speed of the two trains?

## (A) 30 km/h (B) 40 km/h (C) 50 km/h (D) 60 km/h

**Answer:** (A)

**Explanation:** The speed of a train is measured in kilometers per hour (km/h). The speed of the first train is 180 km / 6 hours = 30 km/h. The speed of the second train is 240 km / 8 hours = 30 km/h. The greatest common speed of the two trains is therefore 30 km/h.

**Question 8:** A farmer has 12 oranges and 18 apples. He wants to divide them into equal groups so that each group has the same number of oranges and apples, and the number of groups is as large as possible. What is the largest number of groups that he can create?

## (A) 3 (B) 6 (C) 9 (D) 12

**Answer:** (B)

**Explanation:** The largest number of groups that the farmer can create is the HCF of 12 and 18. The HCF of 12 and 18 is 6. Therefore, the farmer can create 6 groups of 2 oranges and 3 apples each.

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**Question 9 : ****What is the highest common factor of 96 and 404?**

## (A) 3 (B) 4 (C) 9 (D) 12

**Solution:**

**Answer:** (B)

Prime factorization of 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2^{5} × 3

Prime factorization of 404 = 2 × 2 × 101 = 2^{2} × 101

HCF(96, 404) = 22 = 4

Therefore, the highest common factor of 96 and 404 is 4.

**Question 10 : **** What will be the greatest possible length that can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm?**

## (A) 35cm (B) 45cm (C) 95cm (D) 12cm

**Solution:**

**Answer:** (A)

7m = 7 × 100 cm = 700 cm

3m 85 cm = (3 × 100) cm + 85 cm = (300 + 85) cm = 385 cm

12 m 95 cm = (12 × 100) cm + 95 cm = (1200 + 95) cm = 1295 cm

Prime factorization of 700 = 2 x 2 x 5 x 5 x 7

Prime factorization of 385 = 5 x 7 x 11

Prime factorization of 1295 = 5 x 7 x 37

HCF(700, 385, 1295) = 5 x 7 = 35

Therefore, the greatest possible length that can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is 35 cm.

**Question 11 : **** ****Find the numbers if the HCF of two numbers is 29 and their sum is 174.**

## (A) 29 and 145

## (B) 39 and 145

## (C) 49 and 145

## (D) 29 and 155

**Solution:**

**Answer:** (A)

Given that the HCF of two numbers is 29.

Let 29a and 29b be the two required numbers.

According to the given,

29a + 29b = 174

29(a + b) = 174

a + b = 174/29 = 6

The pair of values of co-primes with sum 6 is (1, 5).

So, the possible numbers are:

29 x 1 = 29

29 x 5 = 145

Verification:

Sum of numbers = 29 + 145 = 174

Hence, the required numbers are 29 and 145.

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# More Practice Problems of HCF

## What is the HCF of 12 and 18?

## a) 2

## b) 4

## c) 6

## d) 12

**Answer:** c) 6

**Explanation: ** The HCF of 12 and 18 is the largest number that can exactly divide both 12 and 18. In this case, 6 is the highest common factor.

## Calculate the HCF of 24 and 36.

## a) 6

## b) 12

## c) 18

## d) 48

**Answer:** a) 6

**Explanation: ** The HCF of 24 and 36 is 6 because it is the largest number that can divide both 24 and 36 without leaving a remainder.

## Find the HCF of 15 and 25.

## a) 3

## b) 5

## c) 15

## d) 1

**Answer:** b) 5

**Explanation: ** The HCF of 15 and 25 is 5 because it’s the largest number that can divide both 15 and 25 evenly.

## What is the HCF of 8 and 12?

## a) 2

## b) 4

## c) 8

## d) 12

**Answer:** b) 4

**Explanation: ** The HCF of 8 and 12 is 4, as it is the greatest common factor that can divide both numbers.

## If the HCF of two numbers is 1, what can you conclude?

## a) The numbers are prime.

## b) The numbers are even.

## c) The numbers are odd.

## d) The numbers are negative.

**Answer:** a) The numbers are prime.

**Explanation: ** If the HCF of two numbers is 1, it means they have no common factors other than 1, which implies that they are prime numbers.

## What is the HCF of 0 and 7?

## a) 0

## b) 7

## c) 1

## d) Undefined

**Answer:** b) 7

**Explanation: ** The HCF of 0 and any non-zero number is the non-zero number itself. In this case, it is 7.

## Find the HCF of 28, 42, and 56.

## a) 7

## b) 14

## c) 21

## d) 28

**Answer:** a) 7

**Explanation: ** The HCF of 28, 42, and 56 is 7 because it’s the largest number that can evenly divide all three numbers.

## Calculate the HCF of 72 and 90.

## a) 6

## b) 8

## c) 9

## d) 12

**Answer:** c) 9

**Explanation: ** The HCF of 72 and 90 is 9 because it’s the greatest common factor that can exactly divide both numbers.

## What is the HCF of 15 and 20?

## a) 3

## b) 5

## c) 10

## d) 15

**Answer:** b) 5

**Explanation: ** The HCF of 15 and 20 is 5 because it’s the greatest number that can divide both 15 and 20 evenly.

## Find the HCF of 36 and 48.

## a) 6

## b) 8

## c) 12

## d) 18

**Answer:** c) 12

**Explanation: ** The HCF of 36 and 48 is 12 because it’s the largest number that can exactly divide both numbers.

## Calculate the HCF of 7 and 11.

## a) 1

## b) 2

## c) 3

## d) 7

**Answer:** a) 1

**Explanation: ** The HCF of two prime numbers, such as 7 and 11, is always 1 because prime numbers have no common factors other than 1.

## Find the HCF of 54 and 72.

## a) 6

## b) 9

## c) 12

## d) 18

**Answer:** b) 9

**Explanation: ** The HCF of 54 and 72 is 9 because it’s the largest number that can exactly divide both numbers.

## What is the HCF of 1 and any other positive integer?

## a) 1

## b) 0

## c) The HCF is undefined.

## d) Depends on the other integer.

**Answer:** a) 1

**Explanation: ** The HCF of 1 and any other positive integer is always 1, as 1 is a factor of every positive integer.

## Calculate the HCF of 63, 84, and 105.

## a) 7

## b) 14

## c) 21

## d) 42

**Answer:** a) 7

**Explanation: ** The HCF of 63, 84, and 105 is 7 because it’s the largest number that can evenly divide all three numbers.

## What is the HCF of 36 and 48?

## a) 6

## b) 8

## c) 12

## d) 18

**Answer:** c) 12

**Explanation: ** The HCF of 36 and 48 is 12 because it’s the largest number that can exactly divide both numbers.

## Find the HCF of 64 and 96.

## a) 8

## b) 12

## c) 16

## d) 24

**Answer:** a) 8

**Explanation: ** The HCF of 64 and 96 is 8 because it’s the greatest common factor that can evenly divide both numbers.

# Frequently Asked Questions (FAQs) related to studying for the Sainik School Class 6 Math entrance exam

To help you prepare for Sainik School Class 6 Math, it’s important to use appropriate study materials. Here are some frequently asked questions (FAQ) related to studying for the Sainik School Class 6 Math entrance exam:

**1. What is the syllabus for the Sainik School Class 6 Math entrance exam?**

- The syllabus for the entrance exam may vary slightly from one Sainik School to another. However, it generally covers topics from the standard Class 6 mathematics curriculum, including arithmetic, geometry, algebra, and basic mathematical concepts.

**2. Where can I find official information about the exam pattern and syllabus?**

- You can find official information about the exam pattern and syllabus on the official website of the specific Sainik School you’re applying to. Each school may have its own admission criteria.

**3. Which textbooks should I use for Class 6 Math preparation?**

- You should primarily use the NCERT Class 6 Math textbook. It covers the fundamental concepts and is widely accepted in Indian schools. Additionally, consider supplementary Math textbooks that are designed for competitive exams.

**4. Are there any online resources for Sainik School Class 6 Math preparation?**

- Yes, you can find online resources such as video tutorials, practice questions, and mock tests on educational websites. Websites like ANAND CLASSES offer free Math materials that can be helpful for your preparation.

**5. Where can I get sample papers and previous year’s question papers?**

- You can find sample papers and previous year’s question papers at online bookstore of ANAND CLASSES that sell competitive exam preparation materials. Additionally, ANAND CLASSES website offer downloadable PDFs of these papers for free or at a minimal cost.

**6. Should I consider enrolling in coaching classes for Sainik School Math preparation?**

- Enrolling in ANAND CLASSES is a personal choice. While they can provide structured guidance and additional practice, they are not mandatory. You can achieve success through self-study and the use of appropriate study materials.

**7. How should I manage my study time effectively for Class 6 Math preparation?**

- Create a study schedule that allocates specific time for Math preparation daily. Focus on understanding concepts, practicing regularly, and taking regular breaks to avoid burnout. Consistency is key.

**8. Is there any specific advice for tackling the Math section of the Sainik School entrance exam?**

- Pay close attention to the BODMAS rule (Order of Operations) and practice solving a variety of math problems. Make sure you’re familiar with the types of questions that are commonly asked in the entrance exam.

Remember to check the specific requirements and guidelines provided by the Sainik School you are applying to, as these may vary from school to school.

To prepare effectively for the Sainik School Class 6 Math entrance exam, you should consider the following general sources:

**Sainik School Official Website**: Visit the official website of the Sainik School you are applying to. They often provide information about the exam pattern, syllabus, and sample question papers.**NCERT Textbooks**: The National Council of Educational Research and Training (NCERT) textbooks are widely used in Indian schools and are a valuable resource for exam preparation. Ensure you have the NCERT Math textbook for Class 6.**Solved Sample Papers and Previous Year Question Papers**: You can find solved sample papers and previous year question papers for Sainik School entrance exams at bookstores or online at ANAND CLASSES website. These papers can give you an idea of the exam pattern and types of questions asked.**Math Study Guides**: The Math study guides and reference books are publish under publication department of ANAND CLASSES and are designed to help students prepare for entrance exams. Look for books specifically tailored to the Sainik School entrance exam.**Online Resources**:**www.anandclasses.co.in**

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