# NCERT Solutions for Class 6 Maths Exercise 3.3

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NCERT solutions for Maths Playing with numbers

## NCERT Solutions for Class 6 Maths Playing with numbers

###### 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 1289901586275668663921042971428563060406839 Yes No Yes No No Yes No No No

 Number Divisible by 2 3 4 5 6 8 9 10 11 1289901586275668663921042971428563060406839 YesYesYesNoYesYesYesYesYesNo NoYesNoNoNoYesYesYesYesYes YesNoNoNoNoNoNoYesYesNo NoYesNoYesNoYesNoNoYesNo NoYesNoNoNoYesYesYesYesNo YesNoNoNoNoNoNoYesNoNo NoYesNoNoNoNoYesNoYesNo NoYesNoNoNoYesNoNoYesNo NoYesNoYesNoYesNoNoNoNo

NCERT Solutions for Class 6 Maths Exercise 3.3

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

(a) 572, (b) 726352, (c) 5500, (d) 6000, (e) 12159, (f) 14560, (g) 21084, (h) 31795072, (i) 1700, (j) 2150

(a) 572 {tex} \to {/tex} Divisible by 4 as its last two digits are divisible by 4.

{tex} \to {/tex} Not divisible by 8 as its last three digits are not divisible by 8.

(b) 726352 {tex} \to {/tex} Divisible by 4 as its last two digits are divisible by 4.

{tex} \to {/tex} Divisible by 8 as its last three digits are divisible by 8.

(c) 5500 {tex} \to {/tex} Divisible by 4 as its last two digits are divisible by 4.

{tex} \to {/tex} Not divisible by 8 as its last three digits are not divisible by 8.

(d) 6000 {tex} \to {/tex} Divisible by 4 as its last two digits are 0.

{tex} \to {/tex} Divisible by 8 as its last three digits are 0.

(e) 12159 {tex} \to {/tex} Not divisible by 4 and 8 as it is an odd number.

(f) 14560 {tex} \to {/tex} Divisible by 4 as its last two digits are divisible by 4.

{tex} \to {/tex} Divisible by 8 as its last three digits are divisible by 8.

(g) 21084 {tex} \to {/tex} Divisible by 4 as its last two digits are divisible by 4.

{tex} \to {/tex} Not divisible by 8 as its last three digits are not divisible by 8.

(h) 31795072 {tex} \to {/tex} Divisible by 4 as its last two digits are divisible by 4.

{tex} \to {/tex} Divisible by 8 as its last three digits are divisible by 8.

(i) 1700 {tex} \to {/tex} Divisible by 4 as its last two digits are 0.

{tex} \to {/tex} Not divisible by 8 as its last three digits are not divisible by 8.

(j) 5500 {tex} \to {/tex} Not divisible by 4 as its last two digits are not divisible by 4.

{tex} \to {/tex} 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

(a) 297144 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} 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 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} 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 {tex} \to {/tex} Not divisible by 2 as its units place is not an even number.

{tex} \to {/tex} 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 {tex} \to {/tex} Not divisible by 2 as its units place is not an even number.

{tex} \to {/tex} 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 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} 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 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} Divisible by 3 as sum of its digits (= 27) is not divisible by 3.

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

(g) 1790184 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} Divisible by 3 as sum of its digits (= 30) is not divisible by 3.

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

(h) 12583 {tex} \to {/tex} Not divisible by 2 as its units place is not an even number.

{tex} \to {/tex} 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 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} Divisible by 3 as sum of its digits (= 21) is not divisible by 3.

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

(j) 17852 {tex} \to {/tex} Divisible by 2 as its units place is an even number.

{tex} \to {/tex} 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.

NCERT Solutions for Class 6 Maths Exercise 3.3

###### 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 {tex} \to {/tex} Sum of the digits at odd places = 4 + 5 = 9

{tex} \to {/tex} Sum of the digits at even places = 4 + 5 = 9

{tex} \to {/tex} Difference of both sums = 9 – 9 = 0

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

(b) 10824 {tex} \to {/tex} Sum of the digits at odd places = 4 + 8 +1 = 13

{tex} \to {/tex} Sum of the digits at even places = 2 + 0 = 2

{tex} \to {/tex} Difference of both sums = 13 – 2 = 11

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

(c) 7138965 {tex} \to {/tex} Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24

{tex} \to {/tex} Sum of the digits at even places = 6 + 8 + 1 = 15

{tex} \to {/tex} 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 {tex} \to {/tex} Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17

{tex} \to {/tex} Sum of the digits at even places = 0 + 9 + 1 + 7 = 17

{tex} \to {/tex} Difference of both sums = 17 – 17 = 0

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

(e) 10000001 {tex} \to {/tex} Sum of the digits at odd places = 1 + 0 + 0 + 0 = 1

{tex} \to {/tex} Sum of the digits at even places = 0 + 0 + 0 + 1 = 1

{tex} \to {/tex} Difference of both sums = 1 – 1 = 0

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

(f) 901153 {tex} \to {/tex} Sum of the digits at odd places = 3 + 1 + 0 = 4

{tex} \to {/tex} Sum of the digits at even places = 5 + 1 + 9 = 15

{tex} \to {/tex} 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

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

Therefore, Smallest digit : 2 {tex} \to {/tex} 26724 = 2 + 6 + 7 + 2 + 4 = 21

Largest digit : 8 {tex} \to {/tex} 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 {tex} \to {/tex} 476502 = 4 + 7 + 6 + 5 + 0 + 2 = 24

Largest digit : 9 {tex} \to {/tex} 476592 = 4 + 7 + 6 + 5 + 0 + 2 = 33

NCERT Solutions for Class 6 Maths Exercise 3.3

###### 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 {tex} \to {/tex} 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 {tex} \to {/tex} Odd places = 8 + 9 + 8 = 25

Even places = 6 + 4 + 4 = 14

Difference = 25 – 14 = 11

## NCERT Solutions for Class 6 Maths Exercise 3.3

NCERT Solutions Class 6 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 6 Maths includes text book solutions from Class 6 Maths Book . NCERT Solutions for CBSE Class 6 Maths have total 14 chapters. 6 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 6 solutions PDF and Maths ncert class 6 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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### 6 thoughts on “NCERT Solutions for Class 6 Maths Exercise 3.3”

1. Plz give answer of smallest digit and the largest digit which is divisible by 3

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3. Plz give answer of largest and the smallest digit which is divisible by 3

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