Practice Divisibility Rules Practice Questions with Detailed Solutions – Level 3

The six-digit number 2x534y is divisible by 72, where \(x\) and \(y\) are digits. What is the largest such number?

The five-digit number 5a43b is divisible by 99, where \(a\) and \(b\) are digits. What is the value of \(a + b?\)

What is the largest number that always divides every six-digit number of the form abcabc (for example, 427427)?

A 33-digit number is formed by writing the block 456 eleven times in a row (456456…456). What is the remainder when this number is divided by 7?

The six-digit number 53x572 is divisible by 13. What is the value of the digit \(x?\)

How many six-digit numbers of the form \(3a52b6\) are divisible by 88, where \(a\) and \(b\) are digits?

What is the least number that must be added to 2345678 so that the sum is divisible by 7, 11 and 13?

What is the remainder when 73456281 is divided by 99?

What is the largest five-digit number of the form \(7a5b2\) that is divisible by 36, where \(a\) and \(b\) are digits?

The five-digit number 9a8b7 is divisible by 11, where \(a\) and \(b\) are digits. How many ordered pairs (a, b) are possible?