CBSE Class 6th ( VI) Mathematics Chapter 3. Playing with Numbers :Exercise 3.3

CBSE Class 6th ( VI) Mathematics Chapter 3. Playing with Numbers :Exercise 3.3

1. Using divisibility tests, 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	Yes	No	Yes	No	No	Yes	No	No	No
990	....	....	....	....	....	....	....	....	....
1586	....	....	....	....	....	....	....	....	....
275	....	....	....	....	....	....	....	....	....
6686	....	....	....	....	....	....	....	....	....
639210	....	....	....	....	....	....	....	....	....
429714	....	....	....	....	....	....	....	....	....
2856	....	....	....	....	....	....	....	....	....
3060	....	....	....	....	....	....	....	....	....
406839	....	....	....	....	....	....	....	....	....

Answer: 

Number	Divisible by
	2	3	4	5	6	8	9	10	11
128	Yes	No	Yes	No	No	Yes	No	No	No
990	Yes	Yes	No	Yes	Yes	No	Yes	Yes	Yes
1586	Yes	No	No	No	No	No	No	No	No
275	No	No	No	Yes	No	No	No	No	Yes
6686	Yes	No	No	No	No	No	No	No	No
639210	Yes	Yes	No	Yes	Yes	No	No	Yes	Yes
429714	Yes	Yes	No	No	Yes	No	Yes	No	No
2856	Yes	Yes	Yes	No	Yes	No	No	No	No
3060	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No
406839	No	No	No	No	No	No	No	No	No

2. Using divisibility tests, determine which of the following numbers are divisible by
4; by 8:
(a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159
(f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150
Answer:

Using divisibility tests: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.Divisibility for 1 or 2 digit numbers by 4 has to be checked by actual division.	Numbes Divisible by 4:  (a) 572 (b) 726352 (f) 14560 (g) 21084 (h) 31795072
Using divisibility tests:a number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8. The divisibility for numbers with 1, 2 or 3 digits by 8 has to be checked by actual division.	Numbes Divisible by 8:  (b) 726352 (f) 14560 (h) 31795072

3. Using divisibility tests, determine which of 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
Answer:

Using divisibility tests: Divisiblity by 6 : if a number is divisible by 2 and 3 both then it is divisible by 6 also. Divisiblity by 2 : A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place. Divisiblity by 3 :If the sum of the digits is a multiple of 3, then the number is divisible by 3.

Numbers Divisible by 6:  (a) 297144 (f) 438750 (g) 1790184 (i) 639210

4. Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001
(f) 901153
Answer:

Using divisibility tests: Divisiblity by 11 : To check the divisibility of a number by 11, the rule is, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number.If the difference is either 0 or divisible by 11, then the number is divisible by 11.

Numbers Divisible by 11:  (a) 5445 is divisible by 11 as 5+4=9, 4+5=9 and 9-9=0 (b) 10824 is divisible by 11 as 4+8+1=13, 2+0=2 and 13-2=11 (c) 7138965 is not divisible by 11 as 5+9+3+7=24, 6+8+1=15 and 24-15=9 (d) 70169308 is divisible by 11 as 8+3+6+0=17, 0+9+1+7=17 and 17-17=0 (e) 10000001 is divisible by 11 as 1+0+0+0=1, 0+0+0+1=1 and 1-1=0 (f) 901153 is divisible by 11 as 3+1+0=4, 5+1+9=15 and 15-4=11

5. Write the smallest digit and the greatest digit in the blank space of each of the following
numbers so that the number formed is divisible by 3 :
(a) __ 6724 (b) 4765 __ 2
Answer:

	Number divisible by 3 Using Smallest digit	Number divisible by 3 Using Greatest digit
(a) __ 6724	26724	86724
(b) 4765 __ 2	476532	476592

6. Write a digit in the blank space of each of the following numbers so that the number
formed is divisible by 11 :
(a) 92 __ 389 (b) 8 __ 9484

Answer:	Numbers divisible by 11 Using a digit in blank space
(a) 92 __ 389	924389
(b) 8 __ 9484	869484