GCD Practice Questions Easy Level

The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), of two or more numbers is the largest number that divides all of them exactly, without leaving a remainder.

Key Points:

• It is the greatest number that is a factor of each of the numbers.
• For two numbers a and b, the GCD is the largest number d such that both a ÷ d and b ÷ d are integers.

Read More: Interesting Facts about GCD

Solved Questions on Greatest Common Divisor (Easy)

Question 1: What is the GCD of 12 and 15?

Solution:

Prime factors of 12 and 15:

• 12 = 2² × 3
• 15 = 3 × 5

As only common factor is 3. Thus, GCD = 3

Question 2: GCD of 17 and 19?

Solution:

As 17 and 19 both are prime numbers.

Thus, GCD = 1

Question 3: GCD of 25 and 100?

Solution:

Prime factors:

• 25 = 5⁵
• 100 = 2² × 5²

As only common factor is 25 i.e., 5². Thus, GCD is 5² = 25.

Question 4: GCD of 48, 180, and 240?

Solution:

• 48 = 2⁴× 3
• 180 = 2² × 3² × 5
• 240 = 2⁴ × 3 × 5

As only common factors of all three are 2² × 3. Thus, GCD(48, 180, and 240) = 12.

Question 5: Find the GCD of 18, 27, and 45

Solution:

• Factors of 18: 1,2,3,6,9,18
• Factors of 27: 1,3,9,27
• Common factors: 1,3,9
• GCD = 9

Now, find the GCD of 9 and 45:

• Factors of 9: 1,3,9
• Factors of 45: 1,3,5,9,15,45
• Common factors: 1,3,9
• GCD = 9

Question 6: Find the GCD of 100 and 250

Solution:

Using the prime factorization method:

• Prime factorization of 100: 2^2 \times 5^2
• Prime factorization of 250: 2^1 \times 5^3

The common prime factors are 2^1 and 5^2. So, the GCD is:

2^1 \times 5^2 = 2 \times 25 = 50.

Question 7: Find the greatest common divisor (GCD) or highest common factor (HCF) of 128 and 96.

Solution:

Let's solve this questions using all the three methods we learned about above:

• Prime factors of 128: 2×2×2×2×2×2×2
• Prime factors of 96: 2×2×2×2×2×3

The common prime factors are 2, and the smallest power of 2 common to both numbers is 2⁵.

Thus, \text{HCF} (128, 96) = 2 \times 2 \times 2 \times 2 \times 2 = 32.

Hence, the HCF of 128 and 96 is 32.

Question 8: Find the GCD of 48 and 180.

Solution:

Prime factors of 48: 2^4 \times 3
Prime factors of 180: 2^2 \times 3^2 \times 5

The common prime factors are 2^2 and 3.

= 2² x 3 = 4 x 3 = 12

So, The GCD of 48 and 180 is 12.

Question 9: Find the greatest common factor of 24, 148, and 36.

Solution:

Let's find the greatest common factor of 24, 148, and 36:

• Prime factors of 24: 2×2×2×3
• Prime factors of 148: 2×2×37
• Prime factors of 36: 2×2×3×3

The common prime factors are 2×2

Thus, the greatest common factor is 2×2=4

Hence, the GCD of 24, 148, and 36 is 4.

Question 10: Find the GCD of 56 and 98 using the Euclidean Algorithm

Solution:

The Euclidean algorithm involves dividing the larger number by the smaller and then continuing with the remainder.

1. 98 ÷ 56 = 1 remainder 42
2. 56 ÷ 42 = 1 remainder 14
3. 42 ÷ 14 = 3 remainder 0

Since the remainder is now 0, the GCD is the last non-zero remainder, which is 14.

So, GCD = 14

Practice Questions on GCD

You can download the practice questions with answer key from below:

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GCD Practice Questions Medium Level
GCD Practice Questions Difficult Level