HOMEWORK ON CONGRUENCES SolutionAns11i 1234 divisible by 2

HOMEWORK ON CONGRUENCES

Solution

Ans(11.i):

1234

divisible by 2 = Yes

(because last digit 4 is Even)

divisible by 3 = No

(because sum of all digits i.e. 1+2+3+4=10 is not divisible by 3)

divisible by 4 = No

(because number formed by last two digits i.e. 34 is not divisible by 4)

divisible by 5 = No

(because last digit is neither 0 nor 5)

divisible by 6 = No

(to be divisible by 6, that number must be divisible by 2 and 3 both while it is not divisible by 3)

divisible by 8 = No

(because number formed by last 3 digits i.e. 234 is not divisible by 8)

divisible by 10 = No

(to be divisible by 10, that number must be divisible by 2 and 5 both while it is not divisbile by 5)

divisible by 15 = No

(to be divisible by 15, that number must be divisible by 3 and 5 both while it is not divisbile by 5)

-----------------------------------------------

Ans(11.ii):

6075

divisible by 2 = No

(because last digit 5 is not Even)

divisible by 3 = yes

(because sum of all digits is divisible by 3)

divisible by 4 = No

(because number formed by last two digits i.e. 75 is not divisible by 4)

divisible by 5 = yes

(to be divisible by 5, last digits must be 0 or 5)

divisible by 6 = No

(to be divisible by 6, that number must be divisible by 2 and 3 both while it is not divisible by 2)

divisible by 8 = No

(because number formed by last 3 digits i.e. 075 is not divisible by 8)

divisible by 10 = No

(to be divisible by 10, that number must be divisible by 2 and 5 both while it is not divisbile by 2)

divisible by 15 = Yes

(to be divisible by 15, that number must be divisible by 3 and 5 both.)

-----------------------------------------------

Ans(11.iii):

7560

divisible by 2 = Yes

(because last digit 0 is Even)

divisible by 3 = Yes

(because sum of all digits is divisible by 3)

divisible by 4 = Yes

(because number formed by last two digits i.e. 60 is divisible by 4)

divisible by 5 = Yes

(to be divisible by 5, last digits must be 0 or 5)

divisible by 6 = Yes

(to be divisible by 6, that number must be divisible by 2 and 3 both)

divisible by 8 = Yes

(because number formed by last 3 digits i.e. 560 is divisible by 8)

divisible by 10 = Yes

(to be divisible by 10, that number must be divisible by 2 and 5 both.)

divisible by 15 = Yes

(to be divisible by 15, that number must be divisible by 3 and 5 both)

-----------------------------------------------

-----------------------------------------------

similarly you can do next problem using Divisiblity rules given on the following link

https://en.wikipedia.org/wiki/Divisibility_rule