The answer is 37.

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let the number be 'x' and the divisor be 'd' .

By division algorithm ,

x = dm + 24 .......... (1)

2x = dn + 11 ........... (2)

Multiplying (1) by 2 ,

2x = 2dm + 48 ........ (3)

Equating (2) , (3) ,

dn + 11 = 2dm + 48

dn - 2dm = 48 - 11

d( n - 2m) = 37

Since 37 is a prime number and d,n,m are positive integers , only 2 cases come into consideration -

1) d = 1 ; n - 2m = 37

But if d = 1 , then d | x .

So remainder must be 0 always!

So , d = 1 is not possible.

2) So we are left with the only case , d = 37 , which is possible.

Hence , the required divisor is 37 :)