Question

If 78q928r is divisible by 6, then what are the values of q and r

Answer 1

r should be 2,4,6,8,0
q should satisfy a number such that the sum of no is divisible by 3

Answer 2

Answer:

value of q is 0 , 2  when r is 0 , 2 , 6 , 8 and q is 1 when r is 4

Step-by-step explanation:

Given:

78q928r is divisible by 6

To find: Values of the q and r

Divisibility rule of 6:

A number is divisible by 6 if the given number is divisible by 2 and 3.

Divisibility rule of 2: If a number ends with digit 0 , 2 , 4 , 6 , 8 then the number is divisible by 2

Divisibility rule of 3: If sum of digits of the number is divisible by 3 then the number is divisible by 3.

Given number is divisible by 6.

⇒ It is divisible by 2 and 3 both.

⇒ Value of r = 0 , 2 , 4 , 6 , 8

Now for value of q,

when r = 0

sum of digit of number = 7 + 8 + 9 + 2 + 8 + 0 + q = 34 + q

Now, 34 + q is divisible by 3. ⇒ Value of q = 2

when r = 2

sum of digit of number = 7 + 8 + 9 + 2 + 8 + 2 + q = 36 + q

Now, 36 + q is divisible by 3. ⇒ Value of q = 0

when r = 4

sum of digit of number = 7 + 8 + 9 + 2 + 8 + 4 + q = 38 + q

Now, 38 + q is divisible by 3. ⇒ Value of q = 1

when r = 6

sum of digit of number = 7 + 8 + 9 + 2 + 8 + 6 + q = 40 + q

Now, 40 + q is divisible by 3. ⇒ Value of q = 2

when r = 8

sum of digit of number = 7 + 8 + 9 + 2 + 8 + 8 + q = 42 + q

Now, 42 + q is divisible by 3. ⇒ Value of q = 0

So value of q = 0 , 2  when r = 0 , 2 , 6 , 8 and q = 1 when r = 4

Therefore, value of q is 0 , 2  when r is 0 , 2 , 6 , 8 and q is 1 when r is 4