if 73z 2 is a multiple of 3 where z is a digit then which of the following is a value of z
Answers
Step-by-step explanation:
Given :-
73z2 is a multiple of 3
To find :-
The value of z
Solution :-
Given number = 73z2
Given that it is a multiple of 3
We know that
Divisibility rule by 3:-
The sum of all the digits in a given number is a multiple of 3 then the number is divisible by 3.
The sum of all the digits in 73z2
= 7+3+z+2
= 12+z
12+z is a multiple of 3
So, z = 0, 3,6,9,...
The least possible value of z = 0
Answer :-
The least possible value of z = 0
Check :-
If z = 0 then the number becomes 7302
The sum of all the digits = 7+3+0+2 = 12
12 is a multiple of 3
7302 is a multiple of 3
3 ) 7302 ( 2434
6
______
13
12
_______
10
9
________
12
12
________
0
_________
It is true for z = 0
Verified the given relations in the given problem.
Used formulae:-
Divisibility rule by 3:-
The sum of all the digits in a given number is a multiple of 3 then the number is divisible by 3.
Given :
73z2 is a multiple of 3
To Find :
value of z
Solution :
The sum of all digits in 73z2
= 7 + 3 + z + 2
= 12 + z digits
the possible values of z are :
z = 0 , 3 , 6 , 9 , 12,...
The Least possible value of z is 0.