GCD WORKSHEET SOLUTION1

In this page gcd worksheet solution1 we are going to see solution of some question with clear explanation.

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.

(1) Find the greatest common divisor of

7 x² y z⁴ , 21 x² y⁵ z³

Solution:

= 7 x  x² x y z

= 7 3 x x y x y⁴ x

Therefore the greatest common divisor = 7 x² y z³

(2) Find the greatest common divisor of

x² y,  x³ y , x² y²

Solution:

= x² x y

= x² x y

= x² x y x y

Therefore the greatest common divisor = x² y

(3) Find the greatest common divisor of

25 b c⁴ d³ , 35 b² c⁵ , 45 c³ d

Solution:

= 5 x 5 x b xx d x d x d

= 7 x 5 x b x b xx

= 3 x 3 xxx d

Therefore the greatest common divisor = 5 c³

(4) Find the greatest common divisor of

35 x⁵ y³ z⁴ , 49 x² y z³ , 14 x y² z²

Solution:

= 7 x 5 x x x x x x x x x x x  y y y x z²

= 7 x 7 x x x x x  y x  x z

= 2 x 7 x x x  y x y x

Therefore the greatest common divisor = 7 x y z²

(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

gcd worksheet solution1  gcd worksheet solution1

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