GCD WORKSHEET

GCD worksheet :

Here we are going have to some practice questions. For each question you have solution with detailed explanation.

Definition :

Greatest common divisor (GCD)  is the largest common factor of two or more numbers

To find the greatest common divisor of the given numbers or for algebraic expressions we have to follow the steps:

Step 1 :

List the prime factors of each of the given number. For algebraic expression we have to find factors of them.

Step 2 :

List the common factors of the given numbers or common factors.

Step 3 : 

Multiply those common factors.

Let us have some  problems on this "GCD worksheet".

(1) Find the greatest common divisor of

  7 x² y z⁴ , 21 x² y⁵ z³

Solution

(2) Find the greatest common divisor of

  x² y,  x³ y , x² y²

Solution

(3) Find the greatest common divisor of

  25 b c⁴ d³ , 35 b² c⁵ , 45 c³ d

Solution

(4) Find the greatest common divisor of

  35 x⁵ y³ z⁴ , 49 x² y z³ , 14 x y² z²

Solution

(5) Find the GCD of the following

c² - d² , c (c - d)

Solution

(6) Find the GCD of the following

x⁴ - 27 a³ x , (x - 3a)²

Solution

(7) Find the GCD of the following

m² - 3 m - 18 , m² + 5 m + 6

Solution

(8) Find the GCD of the following

x² + 14 x + 33 , x³ + 10 x² - 11 x

Solution

(9) Find the GCD of the following

x² + 3 x y + 2 y² , x² + 5 x y + 6 y²

Solution

(10) Find the GCD of the following

2 x² - x - 1 , 4 x² + 8 x + 3

Solution

(11) Find the GCD of the following

x² - x - 2 , x² + x - 6 , 3 x² - 13 x + 14

Solution

(12) Find the GCD of the following

x³ - x² + x - 1 , x² + x - 6 , x⁴ - 1

Solution

(13) Find the GCD of the following

24 (6 x⁴ - x³ - 2 x²) , 20 (2 x⁶ + 3 x⁵ + x⁴)

Solution

(14) Find the GCD of the following

(a - 1)⁵ (a + 3)² , (a - 2)² (a - 1)³ (a + 3)⁴

Solution

(15) Find the GCD of the following pairs of polynomials using division algorithm

x³ - 9 x² + 23 x - 15 ,  4 x² - 16 x + 12

Solution

(16) Find the GCD of the following pairs of polynomials using division algorithm

3 x³ + 18 x² + 33 x + 18 ,  3 x² + 13 x + 10

Solution

(17) Find the GCD of the following pairs of polynomials using division algorithm

2 x³ + 2 x² + 2 x + 2 ,  6 x³ + 12 x² + 6 x + 12

Solution

(18) Find the GCD of the following pairs of polynomials using division algorithm

x³ - 3 x² + 4 x - 12 , x⁴ + x³ + 4 x² + 4 x

Solution

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