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**Joy of Mathematics Class 8 Solutions Chapter 6 Playing with Numbers**

Welcome to NCTB Solution. Here with this post we are going to help 8th class students for the Solutions of Joy of Mathematics Class 8 Book, Chapter 6 Playing with Numbers. Here students can easily find step by step solutions of all the problems for Playing with Numbers. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Here students will find solutions for Exercise 6

**Playing with Numbers Exercise 6 Solution : **

**Question no – (1)**

**Solution :**

Divisible by |
||||||||||

Numbers | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

504 | Yes | Yes | Yes | No | Yes | Yes | Yes | Yes | No | No |

750 | Yes | Yes | No | Yes | Yes | No | No | No | Yes | No |

861 | No | Yes | No | No | No | No | No | No | No | Yes |

9999 | No | Yes | No | No | No | No | No | Yes | No | Yes |

31473 | No | Yes | No | No | No | No | No | Yes | No | No |

100001 | No | No | No | No | No | No | No | No | No | Yes |

345675 | No | Yes | No | Yes | No | No | No | No | No | Yes |

**Question no – (2)**

**Solution :**

**(a)** Given, 43180

= A number is divisible by 2 if its units digit is 0.

**∴** 43180, divisible by 2.

**∴** 43180, divisible by 4; (since, its digits at the tens place and units place is divisible by 4)

**∴** (80 ÷ 4 = 20)

**∴** 43180 not divisible by 8; (Since the last three digits of the number 180/8 is not divisible by 8)

**(b)** Given, 578344

= 58344; divisible by 2 [Its unit digit 4 which is divisible by 2]

**∴** 58344; divisible by 4 [Since its last two digits 44 is divisible by 4]

**∴** 58344; divisible by 8 [Since last three digits 344, which is divisible by 8]

**(c)** Given, 65850

= 65850; divisible by 2 [Since its unit digit 0]

**∴** 65850; not divisible by 4 [Since its last two digit 50 is not divisible by 4]

**∴** 65850; not divisible by 8 [Since its last three digits 850, which is not divisible by 8]

**(d)** Given, 35636

= 35636; divisible by 2 [Since, it’s a even number]

**∴** 35636; divisible by 4 [Since, its last two digit 36, which is divisible by 4]

**∴** 35636; not divisible by 8 [∵ Its last three digit 636 is not divisible by 8]

**Question no – (3)**

**Solution :**

**(a)** Given, 564

= 564; divisible by 2 [∵ even number]

**∴** 564 = divisible by 3 [∵ sum of all digits 5 + 6+ 4 = 15, which is divisible by3]

**∴** 564 = divisible by 6 [∵ its divisible by 2 and 3]

**∴** 564 = not divisible by 9 [∵ Sum of all digits = 15, which is not divisible by 9]

**(b)** Given, 31167

= 31167; not divisible by 2 [∵ odd number]

**∴** 31167; divisible by 3 [∵ sum of all digits 3 + 1 + 1 + 6 + 7 = 18, which is divisible by 3]

**∴** 31167; not divisible by 6 [∵ its divisible by 3 but not divisible by 2]

**∴** 31167; divisible by 9 [∵ sum of all digits 3 + 1 + 1 + 6 + 7 = 18, which is divisible by 9]

**(c)** Given, 12348

= 12348; divisible by 2 [∵ even number]

∴ 12348; divisible by 3 [∵ sum of all digits 1 + 2 + 3 + 4 + 8 = 18, which is divisible by 3]

**∴** 12348; divisible by 6 [∵ its divisible by both 2 and 3]

**∴** 12348; divisible by 9 [∵ 18 is divisible by 9]

**(d)** Given, 932160

= 932160; divisible by 2 [∵ its units digits 0]

**∴** 932160; divisible by 3 [∵ sum of all the digits 9 + 3 + 2 + 1 + 6 + 0 = 21, which is divisible by 3]

**∴** 932160; divisible by 6 [∵ its divisible by both 2 and 3]

**∴** 932160; not divisible by 9 [∵ sum of all the digits 21, which is not divisible by 9]

**Question no – (4)**

**Solution :**

**(a)** Given, 27841

= Here, the given number is = 27841

sum of digits at odd places = 2 + 8 + 1 = 11

Sum of digits at even places = 7 + 4 = 11

**∴** Difference = 11 – 11 = 0, which is divisible by11.

**∴** 27841, divisible by 11.

**(b)** Given, 45352

=> Here, the given number is = 45352

Sum of digits at odd places = 4 + 3 + 2 = 9

Sum of digits at even places = 5 + 5 = 10

**∴** Difference = 10 – 9 = 1, which is not divisible by 11.

**∴** 45352, divisible by 11.

**(c)** Given, 237269

= Here, the given number is = 237269

Sum of digits at odd places = 2 + 7 + 6 = 15

Sum of digits at even places = 3 + 2 + 9 = 14

**∴** Difference = 15 – 14 = 1, not divisible by 11

**∴** 237269 is not divisible by 11.

**(d)** Given,589765

= Here, the given number is 589765

Sum of digits at odd places = 5 + 9 + 6 = 20

Sum of digits at even places = 8 + 7 + 5 = 20

**∴** Difference = 20 – 20 = 0, which is divisible by 11

**∴** 589765, divisible by 11.

**Question no – (5)**

**Solution :**

**(a)** Given, 534*

= A number is divisible by 6, when its divisible by 2 and 3

**∴** 5346; divisible by 2 [∵ even number]

**∴** 5346; divisible by 3 [∵ 5 + 3 + 4 + 6 = 18, divisible by 3]

**∴** Replace number is = 5346, which is divisible by 6]

**(b)** Given, 9875*

= A number is divisible by 6, when its divisible by 2 and 3

**∴** 98750; divisible by 2 [∵ last digit 0]

**∴** 98750; divisible by 3 [∵ 9 + 8 + 7 + 5 + 0 = 27, divisible by 3]

**∴** Replace number is 98750, which is divisible by 6.

**(c)** Given, 54*28

= A number is divisible by 6, when its divisible by 2 and 3.

∴ 54228; divisible by 2 [∵ even number]

**∴** 54228; divisible by3 [∵ 5 + 4 + 2 + 2 + 8 = 21, which is divisible by 3]

**∴ **Replace number is 54228, which is divisible by 6.

**(d)** Given, 9207*

= A number is divisible by 6, when its divisible by 2 and 3.

**∴** 92070; divisible by 2 [∵ last digit 0]

**∴** 92070; divisible by 3 [∵ 9 + 2 + 0 + 7 + 0 = 18, divisible by 3]

**∴** Replace number is 92070, which is divisible by 6.

**Question no – (6)**

**Solution :**

**(a)** Given, 6702*

= A number is divisible by 9 when sum of all digits of the number divisible by 9.

6 + 7 + 0 + 2 + 3 = 18, divisible by 9

**∴** Replace number is = 67023

**(b)** Given, *8537

= A number is divisible by 9, when sum of all digits divisible by 9.

* + 8 + 5 + 3 + 7 = * + 23

= 4 + 23

= 27, divisible by 9

**∴** Replace number is = 48537

**(c)** Given, 91*65

= A number is divisible by 9,when sum of all digits divisible by 9.

9 + 1 + * + 6 + 5 = 21 + *

= 21 + 6

= 27, divisible by 9

**∴** Replace number is = 91665

**(d)** Given, 903*8

= A number is divisible by 9, when sum of all digits divisible by 9.

9 + 0 + 3 + * + 8 = 20 + *

= 20 + 7

= 27, divisible by 9

**∴** Replace number is = 90378

**Question no – (7)**

**Solution :**

**(a)** Given, 4536

= A number is divisible by 12, when its divisible by 3 and 4.

4536; divisible by 3 [∵ 4 + 5 + 3 + 6 = 18, divisible by 3]

4536; divisible by 4 [∵ last two digits divisible by 4]

**∴** 4536 divisible by 12.

**(b)** Given, 12348

= A number is divisible by 12, when its divisible by 3 and 4

**∴** 12348; divisible by 3 [∵ 1 + 2 + 3 + 4 + 8 = 18, divisible by 3]

12348; divisible by 4 [∵ last two digit divisible by 4]

**∴** 12348 divisible by 12.

**(c)** Given, 98756

= A number is divisible by 12, when its divisible by 3 and 4

978756, not divisible by 3 [∵ 9 + 8 + 7 + 5 + 6 = 35, not divisible by 3]

98756; divisibleby4 [∵ last two digits divisible by 4]

**∴** 98756 not divisible by 12.

**(d)** Given, 81036

= A number is divisible by 12, when its divisible by 3 and 4

**∴** 81036; divisible by 3 [∵ 8 + 1 + 0 + 3 + 6 = 18, divisible by 3]

81036; divisible by 4 [∵ last two digits divisible by 4]

**∴** 81036 divisible by 12.

**Question no – (8)**

**Solution :**

A number is divisible by 8 and 9 then the number is divisible by 72, because 8 and 9 are co-primes.

**Question no – (10)**

**Solution : **

**(a)** 12 is divisible by 3 and 6 but not by 18.

**(b)** 24 is divisible by 4 and 8 but not by 32.

**(c)** 60 is divisible by 6 and 15 but not by 90.

**(d)** 99 is divisible by 9 and 11 and also by 99.

**Question no – (11)**

**Solution :**

A number divisible by 6 when its divisible by 2 and 3.

43216; divisible by 2

432162; divisible by 3 [∵ 4 + 3 + 2 + 1 + 6 + 2 = 18 which is divisible by 3]

**∴** The smallest number is 2.

**Question no – (12)**

**Solution :**

**(a)** Here, the given number is =724*24

A number is divisible by 8 when last three digits are divisible by 8.

**∴** Here, the last three digit = *24

= 824 [Divisible by 8]

**∴** The largest number is 8.

**(b)** The given number = 724*24

A number is divisible by 9 when sum of all the digits are divisible by 9

7 + 2 + 4 + * + 2 + 4 = 19 + 8

= 27, divisible by 9

**∴** The largest number is 8.

**(c)** The given number is = 724*24

A number is divisible by 11, when,

Sum of digits at odd places = 7 + 4 + 2 = 13

Sum of digits at even places = 2 + * + 4

= 6 + *

= 6 + 7

= 13

**∴** Difference = 13 – 13

= 0, divisible by 11

**∴** The largest number is 7.

**Question no – (13)**

**Solution :**

Greatest number of 3 digits 990, which is divisible by 2 and 5.

**Question no – (14)**

**Solution :**

Greatest number of 4 digits = 9999

a number is divisible by 8 when last three digits divisible by 8.

**∴** The greatest number = 9888, which is divisible by 8.

**Question no – (15)**

**Solution :**

Smallest number of 4 digits = 1000

A number is divisible by 3 when sum of all digits divisible by 3.

**∴** The smallest number is = 1245, which is divisible by 3.

**Previous Chapter Solution : **