Playing with Numbers Class 6 RS Aggarwal Exe-6B Goyal Brothers Prakashan ICSE Foundation Mathematics Solutions. In this article you will learn Factors and Multiples, Divisibility Test. Visit official Website **CISCE** for detail information about ICSE Board Class-6 Mathematics.

## Playing with Numbers Class 6 RS Aggarwal Exe-6B Goyal Brothers Prakashan ICSE Foundation Mathematics Solutions

Board | ICSE |

Publications | Goyal brothers Prakashan |

Subject | Maths |

Class | 6th |

Ch-6 | Playing with Numbers |

Writer | RS Aggrawal |

Book Name | Foundation |

Topics | Solution of Exe-6B |

Academic Session | 2023 – 2024 |

### Factors and Multiples ( Divisibility Test )

Factors are numbers that divide the given number without leaving a remainder. A factor of a number is less than or equal to itself

Multiples are the numbers obtained as a product of a given number and integers. Multiples are always greater than or equal to the given number.

**Exercise- 6B**

**Page- 116,117**

**Que-1: Show that : **

**(i) 15 is a factor of 1065. (ii) 17 is a factor of 1241 (iii) 14 is not a factor of 2186 (iv) 23 is not a factor of 2789**

**Solution- **(i) We can perform the division:

1065/15 = 71

So, 1065 is a factor of 15.

(ii) We can perform division:

1241/17 = 73

So, 1241 is a factor of 17

(iii) We can perform division:

2186/14 = 156.14

So, 2186 is not a factor of 14

(iv) We can perform division:

2789/23 = 121.26

So, 2789 is not a factor of 23.

**Que-2: Write down all the factors of :**

** (i) 40 (ii) 56 (iii) 63 (iv) 84**

**Solution- **(i) 40 = 1,2,4,5,8,10,20,40

(ii) 56 = 1,2,4,7,8,14,28,56

(iii) 63 = 1,3,7,9,21,63

(iv) 84 = 1,2,3,4,6,7,12,14,21,28,42,84

**Que-3: Write down : (i) First six multiples of 7 (ii) First seven multiples of 13 (iii) First five multiples of 19.**

**Solution- **(i) 7,14,21,28,35,42

(ii) 13,26,39,52,65,78,91

(iii) 19,38,57,76,95

**Que-4: Which of the following are prime numbers? 15, 19, 29, 37, 63, 91, 47, 51, 73, 87, 97**

**Solution- **A number that can be divided exactly only by itself and 1 is called prime number.

So, 19,29,37,47,73, and 97 are prime numbers.

**Que-5: (i) Write all prime numbers between 30 and 60. ****(ii) Write all prime numbers between 70 and 100.**

**Solution- **(i) Prime numbers between 30 and 60 are 31,37,41,43,47,53,59.

(ii) Prime numbers between 70 and 100 are 71,73,79,83,89,97.

**Que-6: Express each of the following as a product of prime factors:**

**(i) 105 (ii) 180 (iii) 420 (iv) 462 (v) 1035 (vi) 1197 (vii) 2535 (viii) 4641**

**Solution- **(i) 105 = 3 x 5 x 7

(ii) 180 = 2 x 2 x 3 x 3 x 5

(iii) 420 = 2 x 2 x 3 x 5 x 7

(iv) 462 = 2 x 3 x 7 x 11

(v) 1035 = 3 x 3 x 5 x 23

(vi) 1197 = 3 x 3 x 7 x 19

(vii) 2535 = 5 x 3 x 13 x 13

(viii) 4641 = 3 x 7 x 13 x 17

**Que-7: Fill in the blanks :**

**(i) _____ is a factor of every number (ii) ____ is a multiple of every number
(iii) ____ is the only even prime number.
(iv) _____ is neither prime nor composite.
(v) The last 2-digit prime number is _____
(vi) There are ______ prime numbers between 1 and 100.**

**Solution- **(i) 1, (ii) 0 (iii) 2 (iv) 1 (v) 97 (vi) 25

**Que-8: Which of the following numbers are divisible by 3 ?**

**(i) 57432 (ii) 693503 (iii) 3002002 (iv) 777771**

**Solution- **Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3. So, (i) and (iv) are divisible by 3.

**Que-9: ****Which of the following numbers are divisible by 9 ?**

**(i) 666657 (ii) 999083 (iii) 756432 (iv) 876869**

**Solution- **if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

So, (i) and (iii) are divisible by 9.

**Que-10:** **Which of the following numbers are divisible by 11 ?**

**(i) 22222 (ii) 3303033 (iii) 1589148 (iv) 1302444**

**Solution- **This particular rule states that the given number can only be completely divided by 11 if the difference of the sum of digits at odd position and sum of digits at even position in a number is 0 or 11.

So, (iii) and (iv) are divisible by 11.

**Que-11: ****Which of the following numbers are divisible by 4 ?**

**(i) 36518 (ii) 579012 (iii) 236754 (iv) 907246**

**Solution- **If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely. So, (ii) are divisible by 4.

**Que-12: ****Which of the following numbers are divisible by 8 ?**

**(i) 13756 (ii) 467132 (iii) 6572904 (iv) 972972**

**Solution- **if the last three numbers are zero or divisible by 8, the whole number is divisible by 8.

So, (iii) are divisible by 8.

**Que-13: ****Which of the following numbers are divisible by 6 ?**

**(i) 835704 (ii) 367038 (iii) 630663 (iv) 626266**

**Solution- **A given number is divisible by 6 if it ends with digits 0,2,4,6,8 and the sum of the digits is divisible by 3.

So, (i) and (ii) are divisible by 6.

**Que-14: ****Which of the following numbers are divisible by 7 ?**

**(i) 67102 (ii) 73056 (iii) 102543 (iv) 203647**

**Solution- **the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0. So, (i) and (iii) are divisible by 7.

**Que-15: ****Which of the following numbers are divisible by 5 ? **

**(i) 55513 (ii) 689015 (iii) 37490 (iv) 1010106**

**Solution- **If the last number is either 0 or 5, the entire number is divisible by 5.

So, (ii) and (iii) are divisible by 5.

**Que-16: Separate even and odd numbers out of the following :**

**(i) 267890 (ii) 357941 (iii) 668427 (iv) 200593 (v) 246825 (vi) 489562**

**Solution- **Even numbers are those numbers whose last digit has 0.2,4,6,8.

Odd numbers are those numbers whose last digit has 1,3,5,7

So, (i) and (vi) are even number.

and (ii), (iii), (iv) and (v) are odd number.

**— : end of Playing with Numbers Class 6 RS Aggarwal Exe-6B Goyal Brothers ICSE Maths Solutions :–**

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