### Playing with Numbers-Solutions Ex. 3.3

CBSE Class –VI Mathematics

NCERT Solutions

Chapter 3 Playing With Numbers (Ex. 3.3)

NCERT Solutions

Chapter 3 Playing With Numbers (Ex. 3.3)

Question 1. Using divisibility test, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11. (say yes or no)

Number | Divisible by | ||||||||

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

128 990 1586 275 6686 639210 429714 2856 3060 406839 | Yes | No | Yes | No | No | Yes | No | No | No |

Answer:

Number | Divisible by | ||||||||

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

128 990 1586 275 6686 639210 429714 2856 3060 406839 | Yes Yes Yes No Yes Yes Yes Yes Yes No | No Yes No No No Yes Yes Yes Yes Yes | Yes No No No No No No Yes Yes No | No Yes No Yes No Yes No No Yes No | No Yes No No No Yes Yes Yes Yes No | Yes No No No No No No Yes No No | No Yes No No No No Yes No Yes No | No Yes No No No Yes No No Yes No | No Yes No Yes No Yes No No No No |

Question 2. Using divisibility test, determine which of the following numbers are divisibly by 4; by 8:

(a) 572

(b) 726352

(c) 550

(d) 6000

(e) 12159

(f) 14560

(g) 21084

(h) 31795072

(i) 1700

(j) 2150

(b) 726352

(c) 550

(d) 6000

(e) 12159

(f) 14560

(g) 21084

(h) 31795072

(i) 1700

(j) 2150

Answer:

(a) 572

Divisible by 4 as its last two digits are divisible by 4.

Divisible by 4 as its last two digits are divisible by 4.

Not divisible by 8 as its last three digits are not divisible by 8.

(b) 726352

Divisible by 4 as its last two digits are divisible by 4.

Divisible by 8 as its last three digits are divisible by 8.

(c) 5500

Divisible by 4 as its last two digits are divisible by 4.

Not divisible by 8 as its last three digits are not divisible by 8.

(d) 6000

Divisible by 4 as its last two digits are 0.

Divisible by 8 as its last three digits are 0.

(e) 12159

Not divisible by 4 and 8 as it is an odd number.

(f) 14560

Divisible by 4 as its last two digits are divisible by 4.

Divisible by 8 as its last three digits are divisible by 8.

(g) 21084

Divisible by 4 as its last two digits are divisible by 4.

Not divisible by 8 as its last three digits are not divisible by 8.

(h) 31795072

Divisible by 4 as its last two digits are divisible by 4.

Divisible by 8 as its last three digits are divisible by 8.

(i) 1700

Divisible by 4 as its last two digits are 0.

Not divisible by 8 as its last three digits are not divisible by 8.

(j) 5500

Divisible by 4 as its last two digits are 0.

Not divisible by 8 as its last three digits are not divisible by 8.

Question 3. Using divisibility test, determine which of the following numbers are divisible by 6:

(a) 297144

(b) 1258

(c) 4335

(d) 61233

(e) 901352

(f) 438750

(g) 1790184

(h) 12583

(i) 639210

(j) 17852

(b) 1258

(c) 4335

(d) 61233

(e) 901352

(f) 438750

(g) 1790184

(h) 12583

(i) 639210

(j) 17852

Answer:

(a) 297144

Divisible by 2 as its units place is an even number.

Divisible by 3 as sum of its digits (= 27) is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.

(b) 1258

Divisible by 2 as its units place is an even number.

Not divisible by 3 as sum of its digits (= 16) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(c) 4335

Not divisible by 2 as its units place is not an even number.

Divisible by 3 as sum of its digits (= 15) is divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(d) 61233

Not divisible by 2 as its units place is not an even number.

Divisible by 3 as sum of its digits (= 15) is divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(e) 901352

Divisible by 2 as its units place is an even number.

Not divisible by 3 as sum of its digits (= 20) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(f) 438750

Divisible by 2 as its units place is 0.

Divisible by 3 as sum of its digits (= 27) is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(g) 1790184

Divisible by 2 as its units place is an even number.

Divisible by 3 as sum of its digits (= 30) is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(h) 12583

Not divisible by 2 as its units place is not an even number.

Not divisible by 3 as sum of its digits (= 19) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(i) 639210

Divisible by 2 as its units place is 0.

Divisible by 3 as sum of its digits (= 21) is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(j) 17852

Divisible by 2 as its units place is an even number.

Not divisible by 3 as sum of its digits (= 23) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

Question 4. Using divisibility test, determine which of the following numbers are divisible by 11:

(a) 5445

(b) 10824

(c) 7138965

(d) 70169308

(e) 10000001

(f) 901153

Answer:

(a) 5445

Sum of the digits at odd places = 4 + 5 = 9

Sum of the digits at even places = 4 + 5 = 9

Difference of both sums = 9 – 9 = 0

Since the difference is 0, therefore, the number is divisible by 11.

(b) 10824

Sum of the digits at odd places = 4 + 8 +1 = 13

Sum of the digits at even places = 2 + 0 = 2

Difference of both sums = 13 – 2 = 11

Since the difference is 11, therefore, the number is divisible by 11.

(c) 7138965

Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24

Sum of the digits at even places = 6 + 8 + 1 = 15

Difference of both sums = 24 – 15 = 9

Since the difference is neither 0 nor 11, therefore, the number is not divisible by 11.

(d) 70169308

Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17

Sum of the digits at even places = 0 + 9 + 1 + 7 = 17

Difference of both sums = 17 – 17 = 0

Since the difference is 0, therefore, the number is divisible by 11.

(e) 10000001

Sum of the digits at odd places = 1 + 0 + 0 + 0 = 1

Sum of the digits at even places = 0 + 0 + 0 + 1 = 1

Difference of both sums = 1 – 1 = 0

Since the difference is 0, therefore, the number is divisible by 11.

(f) 901153

Sum of the digits at odd places = 3 + 1 + 0 = 4

Sum of the digits at even places = 5 + 1 + 9 = 15

Difference of both sums = 15 – 4 = 11

Since the difference is 11, therefore, the number is divisible by 11.

Question 5. Write the smallest digit and the largest digit in the blanks space of each of the following numbers, so that the number formed is divisibly by 3:

(a) ____ 6724

(b) 4765 ____ 2

Answer:

(a) We know that a number is divisible by 3 if the sum of all digits is divisible by 3.

Therefore, Smallest digit : 2 26724 = 2 + 6 + 7 + 2 + 4 = 21

Largest digit : 8 86724 = 8 + 6 + 7 + 2 + 4 = 27

(b) We know that a number is divisible by 3 if the sum of all digits is divisible by 3.

Therefore, Smallest digit : 0 476502 = 4 + 7 + 6 + 5 + 0 + 2 = 24

Largest digit : 9 476592 = 4 + 7 + 6 + 5 + 0 + 2 = 33

Question 6. Write the smallest digit and the largest digit in the blanks space of each of the following numbers so that the number formed is divisibly by 11:

(a) 92 ____ 389

(b) 8 ____9484

Answer:

(a) We know that a number is divisible by 11 if the difference of the sum of the digits at odd

places and that of even places should be either 0 or 11.

Therefore, 928389

Odd places = 9 + 8 + 8 = 25

Even places = 2 + 3 + 9 = 14

Difference = 25 – 14 = 11

(b) We know that a number is divisible by 11 if the difference of the sum of the digits at odd

places and that of even places should be either 0 or 11.

Therefore, 869484

Odd places = 8 + 9 + 8 = 25

Even places = 6 + 4 + 4 = 14

Difference = 25 – 14 = 11