## Saturday, 10 March 2012

### 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 .... .... .... .... .... .... .... .... ....

 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
 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

 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

 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