Question

Find x if 59x Is divisible by 6. Explain it

Answer 1

Answer:

LCM of 59 and 6 is 354, which is sixth multiple of 59.

Therefore, as the smallest number divisible by 59 and 6 both is 354, x can have the smallest value of 6 - for 59x to be divisible by it.

Answer 2

Step-by-step explanation:

Given :-

59x Is divisible by 6

To find :-

Find x ?

Solution :-

Given number = 59x

Given that 59x is divisible by 6

We know that

If a number is divisible by 6 then it is divisible by both 2 and 3.

So , 59x is divisible by both 2 and 3

If a number is divisible by 2 if it has one of the digits 0,2,4,6,8 in its ones place.

The unit place must be one of the digits 0,2,4,6,8

The possible values of x = 0,2,4,6,8

And

If a number is divisible by 3 then the sum of all the digits divisible by 3

=> Sum of the digits

=> 5+9+x

=> 14+x

So the multiple of 3 comes after the number = 15,18,21...

18 is the multiple of 3 which is also divisible by 2

=> 14+x = 18

=> x = 18-14

=> x = 4

Therefore x = 4

Answer:-

The value of x for the given problem is 4

Check:-

If x = 4 then the number becomes 594

Since the ones place is 4 it is divisible by 2

The sum of the digits = 5+9+4=18

Which is divisible by 3

So 594 is divisible by both 2 and 3

594 is divisible by 6

Verified the given relations in the given problem.

Used formulae:-

Divisibility by 2:-

• If a number is divisible by 2 if it has one of the digits 0,2,4,6,8 in its ones place.

Divisibility by 3:-

• If a number is divisible by 3 then the sum of all the digits divisible by 3

Divisibility by 6:-

• If a number is divisible by 6 then it is divisible by both 2 and 3.