Write down any three-digit number (for example, 425). Examine why they work ?
Make a six-digit number by repeating these digits in the same order (425425). Your new number is divisible by 7, 11, and 13.

How many three-digit numbers are divisible by 7?

Find the sum of all three digit natural numbers divisible by 7

How many three digit numbers are divisible by 7 ?

How many three-digit numbers can be made using the digits 0, 1, 2, …, 9, if no digit is repeated ?

Find the greatest number of 7 digits which is exactly divisible by 12, 15 and 21.

Find the sum of all three digit numbers which are multiples of 11.

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?

How many four-digit numbers can be formed by using the digits 1, 2, 3, 4, 5, 6, 7 if at least one digit is repeated.

Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

How many three digit numbers are such that when divided by 7, leaves a remained 3 in each case ?