Curriculum
GRADE VIII MATHS
Chapters
0/14
-
Square And Cube
Preview -
Power Play
Preview
-
Story Of Numbers
Preview
-
Quadrilaterals
Preview
-
Number Play
Preview
-
Distribute Mutiply
Preview
-
Proportional Reasoning 1
Preview
-
Fraction In Disguise
Preview
-
Baudhayana-Pythagoras
Preview
-
Proportional Reasoning 2
Preview
-
Geometric Themes
Preview
-
Dots And Lines
Preview
-
Algebra Play
Preview
-
Area
Preview
Number Play
School Revise · Grade 8 · Maths · Chapter 5 · Ganita Prakash
Number Play
Maths, Class 8, Ganita Prakash. Numbers hide neat patterns. This chapter plays with multiples, quick divisibility checks, and digit puzzles where letters stand in disguise for digits.
|
|
||
|
|
What this chapter is about
Is a number a multiple of 3 without dividing? Can a puzzle with hidden digits be solved? In this chapter we explore multiples, learn quick divisibility rules, and crack digit puzzles where symbols stand for digits in disguise.
1. Multiples and quick divisibility
|
Divisibility rules a number is a multiple of another if it divides exactly, leaving no remainder; quick rules save dividing: a number is divisible by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, by 10 if it ends in 0, and by 3 or 9 if the sum of its digits is For 3 and 9, keep adding the digits until a small number remains, then check that. These rules come from how place value splits a number into tens, hundreds and so on. In real life: A shopkeeper can share 453 sweets equally among 3 children without dividing, because 4 + 5 + 3 = 12 is a multiple of 3. |
|
Worked example 1 Question. Is 453 divisible by 3?
Answer: Yes, 453 is divisible by 3, because its digit sum 12 is. |
2. Digits in disguise
|
Digits in disguise in a digit puzzle each letter stands for a single digit; using place value and divisibility clues we work out which digit each letter must be We reason step by step: a carry, an even ending or a known digit sum narrows the choices until only one digit fits each letter. In real life: Newspaper puzzles where SEND + MORE = MONEY hide digits behind letters in just this way. |
|
Worked example 2 Question. In the two-digit number 2A, the whole number is divisible by 5. What can A be?
Answer: A can be 0 or 5. |
|
Worked example 3 Question. Is 1 234 divisible by 9?
Answer: No, because the digit sum 10 is not divisible by 9. |
Practise with the interactive
Practise it: type a number and watch the divisibility rules light up, then solve a small digit puzzle by testing each rule. The interactive opens right here in the lesson.
Practice set A, multiple choice
1. A number is divisible by 5 if it ends in …
0 or 5.
2. To test divisibility by 3, we …
Add the digits and check if that sum is a multiple of 3.
3. 90 is a multiple of …
2, 3, 5, 9 and 10, among others (its digit sum is 9 and it ends in 0).
4. A digit puzzle uses letters to stand for …
Single digits, hidden in disguise.
Practice set B, short answer
1. Is 738 divisible by 9?
| 1 | Add the digits, 7 + 3 + 8 = 18. which is a multiple of 9. |
| 2 | So. yes, 738 is divisible by 9. |
2. List two multiples of 6 between 20 and 40.
24 and 30 (also 36).
3. A three-digit number ends in 0. Give two numbers it must divide by.
2, 5 and 10 all divide it, since it ends in 0.
Quick summary
| Idea | The idea |
| Multiple | divides exactly, no remainder. |
| By 2 | ends in an even digit. |
| By 5 | ends in 0 or 5. |
| By 10 | ends in 0. |
| By 3 or 9 | use the digit sum. |
| Digit puzzle | letters are digits in disguise. |
| Open the Virtual Lab |
These free Grade 8 Maths revision notes explain multiples, quick rules for divisibility, and digit puzzles in disguise, with clear step by step worked examples and labelled diagrams for every student following the new Ganita Prakash book.
© 2026 School Revise. All rights reserved. This lesson is original content written by School Revise, aligned to the CBSE and NCERT Class 8 Mathematics (Ganita Prakash) syllabus. Unauthorised copying, reproduction or redistribution is not permitted. Curriculum names are used only to indicate alignment.
Google