If a square number is divisible only by 13 and 15 then what are the last two digits of the number?

Question

Can anyone please solve the problem below:

If a square number is divisible only by 13 and 15 then what are the last two digits
of the number?

Answer 1

Hi Akash, for a number to be divisible by 13 and 15, we can eliminate all square numbers that do not end in 0 or 5. 

 

More importantly, since 13 and 15 are prime numbers, we only have to look for a number, not its square, that is divisible by 13 and 15 that ends in 0 or 5.

 

One such number is 13 * 15, or 195.

 

Since 13 and 15 divide into 195, they will also divide in to multiples of 195.

 

Square 195 gives 38025, were the last digit ends in a 5 and is divisible by 13, and 15.

 

Answer: the last two digits are 25.

 

Questions?