Question

find the smallest multiple of 15 such that , each digit of the multiple is either 0 or 8.

Answer 1

4 answers · Mathematics 

 Best Answer

to know the multiple of 15 

we get the co prime factors of 15, (co prime factors are those which do not have any common factors e.g 12 has 4 and 3 and these factors need not be prime one) here 15 co primes are 5 and 3 by the way they are prime also. so it is very good 

Now see the divisibility rule of these factors 

as for 5: any Number divisible by 5 the last digit should be either 0 or 5 

eg, 30000, 511115 2323235 3232320 etc 

and for divisibility by 3: the sum of digits should be 3 
as 3, 18, 51, 120000, 21212121 111, 10000100001. 

so in the case as the number is having 0 and 8 only so last dist has to be 0. 

now how many 8 you need in smallest number. just add them which are having the sum which is divisible by 3, and that can be number 3 times and 8 is even no and con never be divisible by 3 itself 

8+8+8 =24 divisible by 3 

so our answer is 8880