What is the value of a so that the seven−digit number 4645a52 is divisible by 72?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1.
When a number is divisible by 72 it means that it is divisible by 8 and 9
Divisibility rule of 8: A number is divisible by 9 if the last three digits are divisible by 8.
Divisibility rule of 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
The number is 4645a52
so, 4 + 6 + 4 + 5 + a + 5 + 2 = 26 + a must be divisible by 9
Thus, for the value of a = 1
a52 = 152 is divisible by 8 and 9 also
Thus, a = 1