Maths-4 HCF (Highest Common Factor ) : Questions and Step-by-Step Solutions for Competitive Exams (SSC, BSSC, Bank,Railways)

Maths-4 HCF (Highest Common Factor ) : Questions and Step-by-Step Solutions for Competitive Exams (SSC, BSSC, Bank,Railways)

HCF (Highest Common Factor) from the very basics in clear, easy steps. This is a must-know concept for number-based questions in CDS, SSC, and other exams.

What is HCF?

HCF is the largest number that divides two or more numbers exactly (without leaving a remainder).
It’s also called GCD (Greatest Common Divisor).

Step-by-Step Method to Find HCF

Method 1: Prime Factorization (Best for small numbers)

Example: Find HCF of 12 and 18

Step 1: Write prime factors

• 12 = 2 × 2 × 3
• 18 = 2 × 3 × 3

Step 2: Take only the common prime factors

• Common = 2 × 3 = 6

Method 2: Division Method (Best for large numbers)

Example: Find HCF of 36 and 60

Step 1: Divide larger by smaller

• 60 ÷ 36 = remainder 24
• 36 ÷ 24 = remainder 12
• 24 ÷ 12 = remainder 0
  When remainder is 0, the last divisor is the HCF = 12

Method 3: Listing Factors (Good for small numbers)

Example: Find HCF of 8 and 12

Step 1: List all factors

• 8 → 1, 2, 4, 8
• 12 → 1, 2, 3, 4, 6, 12

Step 2: Find the largest common factor

• Common = 1, 2, 4 → HCF = 4

Quick Tips

• HCF is always equal to or smaller than the smallest number.
• Use HCF when dividing things equally or finding common measures.
• For two numbers:
  HCF × LCM = Product of the numbers

Here’s a complete set of 20 HCF (Highest Common Factor) practice questions with step-by-step solutions, starting from basic and progressing to intermediate and word problems. These are perfect for strengthening your number sense and boosting your exam prep.

HCF Practice Questions with Step-by-Step Solutions

🔹 Basic Level

1. Find the HCF of 4 and 6

Step 1:

• 4 = 2 × 2
• 6 = 2 × 3

Step 2:

• Common factor = 2
  HCF = 2

2. Find the HCF of 5 and 10

Step 1:

• 5 = 5
• 10 = 2 × 5

Step 2:

• Common factor = 5
  HCF = 5

3. Find the HCF of 8 and 12

Step 1:

• 8 = 2 × 2 × 2
• 12 = 2 × 2 × 3

Step 2:

• Common = 2 × 2 = 4
  HCF = 4

4. Find the HCF of 9 and 15

Step 1:

• 9 = 3 × 3
• 15 = 3 × 5

Step 2:

• Common = 3
  HCF = 3

5. Find the HCF of 14 and 21

Step 1:

• 14 = 2 × 7
• 21 = 3 × 7

Step 2:

• Common = 7
  HCF = 7

🔹 Intermediate Level

6. Find the HCF of 18 and 24

Step 1:

• 18 = 2 × 3 × 3
• 24 = 2 × 2 × 2 × 3

Step 2:

• Common = 2 × 3 = 6
  HCF = 6

7. Find the HCF of 36 and 60 using division method

Step 1:

• 60 ÷ 36 = remainder 24
• 36 ÷ 24 = remainder 12
• 24 ÷ 12 = remainder 0
  HCF = 12

8. Find the HCF of 45 and 75

Step 1:

• 45 = 3 × 3 × 5
• 75 = 3 × 5 × 5

Step 2:

• Common = 3 × 5 = 15
  HCF = 15

9. Find the HCF of 48 and 64

Step 1:

• 48 = 2⁴ × 3
• 64 = 2⁶

Step 2:

• Common = 2⁴ = 16
  HCF = 16

10. Find the HCF of 27 and 36

Step 1:

• 27 = 3 × 3 × 3
• 36 = 2² × 3²

Step 2:

• Common = 3² = 9
  HCF = 9

🔹 Three Numbers

11. Find the HCF of 12, 18, and 24

Step 1:

• 12 = 2² × 3
• 18 = 2 × 3²
• 24 = 2³ × 3

Step 2:

• Common = 2 × 3 = 6
  HCF = 6

12. Find the HCF of 30, 45, and 60

Step 1:

• 30 = 2 × 3 × 5
• 45 = 3 × 3 × 5
• 60 = 2² × 3 × 5

Step 2:

• Common = 3 × 5 = 15
  HCF = 15

13. Find the HCF of 16, 24, and 32

Step 1:

• 16 = 2⁴
• 24 = 2³ × 3
• 32 = 2⁵

Step 2:

• Common = 2³ = 8
  HCF = 8

14. Find the HCF of 20, 25, and 30

Step 1:

• 20 = 2 × 2 × 5
• 25 = 5 × 5
• 30 = 2 × 3 × 5

Step 2:

• Common = 5
  HCF = 5

15. Find the HCF of 18, 27, and 36

Step 1:

• 18 = 2 × 3²
• 27 = 3³
• 36 = 2² × 3²

Step 2:

• Common = 3² = 9
  HCF = 9

🔹 Word Problems

16. Two ropes are 12 meters and 18 meters long. What is the greatest length that can be used to cut both ropes without leftover?

Step 1:

• HCF of 12 and 18 = 6
  Answer: 6 meters

17. A gardener has 30 tulips, 45 roses. He wants to make bouquets with equal number of each flower. What is the maximum number of bouquets?

Step 1:

• HCF of 30 and 45 = 15
  Answer: 15 bouquets

18. A teacher has 36 pencils and 60 pens. What is the largest number of students who can get equal sets?

Step 1:

• HCF of 36 and 60 = 12
  Answer: 12 students

19. A rectangular floor is 48 m by 60 m. What is the largest square tile that can be used to tile the floor without cutting?

Step 1:

• HCF of 48 and 60 = 12
  Answer: 12 m tile

20. Three bells ring every 15, 20, and 25 minutes. What is the greatest time interval after which they will ring together?

Step 1:

• HCF of 15, 20, 25 = 5
  Answer: 5 minutes

Please practice at least 20 similar questions daily or twice a week