**1. Find the common factors of :**

(a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120

(a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120

**Answer:**

**2. Find the common factors of :**

(a) 4, 8 and 12 (b) 5, 15 and 25

(a) 4, 8 and 12 (b) 5, 15 and 25

**Answer:**

(a) 4, 8 and 12 | |

Factors of 4 are: | 1, 2, 4 |

Factors of 8 are: | 1, 2, 4, 8 |

Factors of 12 are: | 1, 2, 3, 4, 6, 12 |

Common factors of 4, 8 and 12 are 1, 2, 4 | |

(b) 5, 15 and 25 | |

Factors of 5 are: | 1, 5 |

Factors of 15 are: | 1, 5, 15 |

Factors of 25 are: | 1, 5, 25 |

Common factors of 5, 15 and 25 are 1, 5 |

**3. Find first three common multiples of :**

(a) 6 and 8 (b) 12 and 18

(a) 6 and 8 (b) 12 and 18

**Answer:**

(a) 6 and 8 | |

multiples of 6 are: | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 |

multiples of 8 are: | 8, 16, 24, 32, 40, 48, 56, 64, 72, 180 |

Common multiples of 6 and 8 are: 24, 48, 72 | |

(b) 12 and 18 | |

multiples of 12 are: | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 |

multiples of 18 are: | 18, 36, 54, 72, 90, 108, 126, 144, 162, 180 |

Common multiples of 12 and 18 are 36, 72, 108 |

**4. Write all the numbers less than 100 which are common multiples of 3 and 4.**

**Answer:**

Numbers less than 100 which are multiples of 3 are | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48,51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 96, 99 |

Numbers less than 100 which are multiples of 4 are | 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 , 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 |

The numbers less than 100 which are common multiples of 3 and 4 are 12, 24, 36, 48, 60, 72, 84 and 96 |

**5. Which of the following numbers are co-prime?**

(a) 18 and 35 (b) 15 and 37 (c) 30 and 415

(d) 17 and 68 (e) 216 and 215 (f) 81 and 16

(a) 18 and 35 (b) 15 and 37 (c) 30 and 415

(d) 17 and 68 (e) 216 and 215 (f) 81 and 16

**Answer:**

We know that Two numbers having only 1 as a common factor are called co-prime numbers. | |

Factor of 18 are | 1, 2, 3, 6, 9 |

Factor of 35 are | 1, 5, 7 |

As the common factor of 18 and 35 is just 1, there for 18 and 35 are co-prime numbers | |

(b) 15 and 37 | |

Factor of 15 are | 1, 5, 15 |

Factor of 37 are | 1, 37 |

As the common factor of 15 and 37 is just 1, there for 15 and 37 are co-prime numbers | |

Factor of 30 are | 1, 2, 3, 5, 6, 10, 15, 30 |

Factor of 415 are | 1, 5, 15, 415 |

As the common factor of 30 and 415 are 1, 5, 15 there for 30 and 415 are not co-prime numbers | |

Factor of 17 are | 1,17 |

Factor of 68 are | 1, 2, 4, 17 |

As the common factor of 17 and 68 are 1,17 there for 17 and 68 are not co-prime numbers | |

Factor of 216 are | 1, 2, 8, 108, 216 |

Factor of 215 are | 1, 5, 15 |

As the common factor 216 and 215 is just 1,there for 216 and 215 are co-prime numbers | |

Factor of 81 are | 1, 3, 9, 27, 81 |

Factor of 16 are | 1, 2, 4, 8 |

As the common factor 81 and 16 is just 1, there for 81 and 16 are co-prime numbers |

**6. A number is divisible by both 5 and 12. By which other number will that number be**

always divisible?

always divisible?

**Answer:**

(a) 5 and 12 | |

multiples of 5 are: | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 |

multiples of 12 are: | 12, 24, 36, 48, 60 |

Common multiple of 5 and 12 is 60,hence 60 is that number | |

60 is divisible by 1, 2, 3, 4, 5, 6, 10, 60 |

**7. A number is divisible by 12. By what other numbers will that number be divisible?**

**Answer:**

Number divisible by 12 are Multples of 12 i.e 12,24,36,48,60,72,84,96,108,120 |

Out of these posible numbers which are multiples of 12, the numbers will be divisible by every factor of that number For example here 60 is a multple of 12 thus divisible by 12 and also divisible by its factors like 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 |

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