Question

Q6) Replace Z by any digit so that 123Z is divisible by
2,3,5,6 and 10​

Answer 1

Answer:

z = 0

Step-by-step explanation:

to make the no. divisible by 10, last digit should be 0

so now, 1230 is divisible by 2,3,5,6 and 10

Answer 2

Given :   123Z  Divisible by 2 , 3 , 5 , 6 , 10

To Find : Value of Z

Solution :

A number is divisible by 2 if

last digit is 0 , 2, 4 , 6 , 8

possible value of Z = 0 , 2 , 4 , 6 , 8

Divisible by  3

if sum of digits is divisible by 3

1 + 2 + 3 + Z is divisible by 3

=> 6 + Z is divisible by 3

possible value of Z   = 0 , 3 , 6

Divisible by  5

if last Digit is 5 or 0

possible value of Z   = 0 , 5

Common in all is 0

if a number is divisible by 2 & 3 then it would be divisible by 6

if a number is divisible by 2 & 5 then it would be divisible by 10

Value of Z = 0

Verification

1230 / 2  = 615

1230/3 =  410

1230/5  = 246

1230/6  = 205

1230/10 = 123

Z = 0  if 123Z is divisible by 2,3,5,6 and 10​

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