Innings2
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Chapter 15: Playing with Numbers

    Introduction

    Divisibility Rules

    Some More Divisibility Rules

    Puzzles Based on Divisibility Rules

    Fun with 3-Digit Numbers

    Puzzles with Missing Digits

    Finding of Divisibility by taking Remainders of Place Values

    Some More Puzzles on Divisibility Rules

    Finding Sum of Consecutive Numbers

    Exercise 15.1

    Exercise 15.2

    Exercise 15.3

    Exercise 15.4

    Exercise 15.5

    Exercise 15.6

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

Chapter 15: Playing with Numbers > Some More Puzzles on Divisibility Rules

Some More Puzzles on Divisibility Rules

Take any 4-digit number, say 1567, and reverse the digits to get a new 4-digit number (7651). Check if the number formed is divisible by both 4 and 5.

Instructions

Divisibility by 4: A number is divisible by 4 if the last digits form a number divisible by 4. The last digits of 7651 are .
51 ÷ 4 = with remainder , so 51 divisible by 4.
Divisibility by 5: A number is divisible by 5 if its last digit is either or .
The last digit of 7651 is , so 7651 divisible by 5.
7651 is not divisible by both 4 and 5.

Take a 3-digit number, like 528. Write it twice to form a 6-digit number (528528). Is the number divisible by 3 and 9?

Instructions

Divisibility by 3: A number is divisible by 3 if the of its digits is divisible by 3. The digits of 528528 are + + + + + = .
30 ÷ 3 = , so 528528 divisible by 3.
Divisibility by 9: A number is divisible by 9 if the of its digits is divisible by 9.
30 ÷ 9 = with remainder , so 528528 divisible by 9.
528528 is divisible by 3 but not by 9.

Take any 3-digit number, say 672. Multiply it by 100 (67200) and subtract the original number (67200 - 672 = 66528). Check if the result is divisible by both 2 and 8.

Instructions

Divisibility by 2: A number is divisible by 2 if its last digit is .
The last digit of 66528 is , which is even, so 66528 divisible by 2.
Divisibility by 8: A number is divisible by 8 if the last digits form a number divisible by 8. The last digits of 66528 are .
528 ÷ 8 = , so 528 divisible by 8.
66528 is divisible by both 2 and 8.

Take a 4-digit number, for example, 2316. Reverse the digits to form another 4-digit number (6132). Add the two numbers together (2316 + 6132). Check if the sum is divisible by both 6 and 12.

Instructions

Addition: 2316 + 6132 =
Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3. The last digit of 8448 is (), so 8448 divisible by 2. The sum of digits is 8 + 4 + 4 + 8 = , which divisible by 3.
Therefore, 8448 divisible by 6.
Divisibility by 12: A number is divisible by 12 if it is divisible by both and . 8448 divisible by 3. The last two digits of 8448 are , which divisible by 4.
Therefore, 8448 divisible by 12.
8448 is divisible by both 6 and 12.