question_answer 1)

Determine, if 25110 is divisible by 45. [Hint 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9]. TIPS If a number is divisible by two co-prime numbers, then it is divisible by their product also.                

Answer:

                We have, \[45=5\times 9,\]also 5 and 9 are co-prime. Now, 25110 is divisible by 5 because its units digit is 0. Again, sum of the digits = 2 + 5 + 1 + 1 + 0 = 9 \[\because \] Sum of the digits is divisible by 9, so 25110 is also divisible by 9. Since, 25110 is divisible by both 5 and 9, where 5 and 9 are co-primes. \[\therefore \] 25110 is divisible by \[5\times 9\] i.e. by 45.