**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 | |

(2) Find the greatest common divisor of x² y, x³ y , x² y² | |

(3) Find the greatest common divisor of 25 b c⁴ d³ , 35 b² c⁵ , 45 c³ d | |

(4) Find the greatest common divisor of 35 x⁵ y³ z⁴ , 49 x² y z³ , 14 x y² z² | |

(5) Find the GCD of the following c² - d² , c (c - d) | |

(6) Find the GCD of the following x⁴ - 27 a³ x , (x - 3a)² | |

(7) Find the GCD of the following m² - 3 m - 18 , m² + 5 m + 6 | |

(8) Find the GCD of the following x² + 14 x + 33 , x³ + 10 x² - 11 x | |

(9) Find the GCD of the following x² + 3 x y + 2 y² , x² + 5 x y + 6 y² | |

(10) Find the GCD of the following 2 x² - x - 1 , 4 x² + 8 x + 3 | |

(11) Find the GCD of the following x² - x - 2 , x² + x - 6 , 3 x² - 13 x + 14 | |

(12) Find the GCD of the following x³ - x² + x - 1 , x² + x - 6 , x⁴ - 1 | |

(13) Find the GCD of the following 24 (6 x⁴ - x³ - 2 x²) , 20 (2 x⁶ + 3 x⁵ + x⁴) | |

(14) Find the GCD of the following (a - 1)⁵ (a + 3)² , (a - 2)² (a - 1)³ (a + 3)⁴ | |

(15) Find the GCD of the following pairs of polynomials using division algorithm x³ - 9 x² + 23 x - 15 , 4 x² - 16 x + 12 | |

(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 | |

(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 | |

(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 |

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