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Tamil Nadu (TNBSE)Class 6 Mathematics★ 3-6 marks in the TN Class 6 Term 3 exam through ordering and Euclid's-algorithm questions

Information Processing (Term 3) - Ordering and Algorithms

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 3 Chapter 5, Information Processing. Arranging things in order, iterative (repeating) processes, Euclid's division algorithm for finding the HCF and Euclid's game, with worked examples, exercises and quick revision.

⏱ 13 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Arrange things in a sensible order
2Explain an iterative process
3Apply Euclid's division algorithm for the HCF
4Understand Euclid's game
5Follow step-by-step procedures

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Why this chapter matters

Ordering data and following step-by-step algorithms like Euclid's are key reasoning and computing skills. These are tested in the TN Class 6 Term 3 exam and build algorithmic thinking.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Term 2 — Numbers (Factors and Multiples)

HCF and division.

Information Processing (Ordering and Algorithms) — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 3 — Chapter 5. Ordering, repeating steps and Euclid's algorithm.

1. About this chapter

This chapter covers arranging things in order, iterative (repeating) processes, Euclid's division algorithm for the HCF, and Euclid's game.

2. Arranging and ordering

Arranging things in order (smallest to largest or by a rule) makes information easy to find and compare — like a dictionary or a class list.
A clear order avoids confusion and helps in searching and sorting.

3. Iterative processes

An iterative process is one that repeats the same step again and again until a condition is met.
Example: repeatedly subtracting or dividing until you reach a stopping point — each repeat is one iteration.

4. Euclid's division algorithm and game

Euclid's division algorithm finds the HCF of two numbers by repeated division:
1. Divide the larger by the smaller and note the remainder.
2. Replace the larger by the smaller and the smaller by the remainder.
3. Repeat until the remainder is 0; the last divisor is the HCF.
Euclid's game is a number game based on repeatedly subtracting multiples — an iterative process that also leads to the HCF.

5. Worked examples

Example 1. Use Euclid's algorithm to find the HCF of 48 and 18. 48 = 18 × 2 + 12; 18 = 12 × 1 + 6; 12 = 6 × 2 + 0 → HCF = 6.

Example 2. What is an iterative process? One that repeats the same step until a condition is met.

Example 3. Arrange in ascending order: 34, 12, 27, 8. 8, 12, 27, 34.

6. Exercises (Samacheer Kalvi)

Arrange in descending order: 56, 23, 78, 9, 41.
Use Euclid's division algorithm to find the HCF of 36 and 24.
Find the HCF of 60 and 48 by repeated division.
Describe one everyday example of an iterative process.
Sort the names Asha, Ravi, Bala, Kavi in alphabetical order.

7. Common mistakes

Mistake: Stopping Euclid's algorithm before the remainder is 0. Fix: Keep dividing until the remainder is 0; the last divisor is the HCF.
Mistake: Taking the last remainder (0) as the HCF. Fix: The HCF is the last non-zero divisor, not the 0 remainder.
Mistake: Ordering carelessly. Fix: Use a clear rule (size or alphabetical) and check each item.

8. Quick revision

Term 3 · Ch 5 · ordering and algorithms.
Arranging in order makes information easy to find and compare.
An iterative process repeats the same step until a condition is met.
Euclid's algorithm: divide, replace, repeat until remainder 0; the last divisor is the HCF.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Ordering

arrange by size or by rule (alphabetical)

Easy to search.

Iterative process

repeat the same step until a condition is met

Each repeat = an iteration.

Euclid's algorithm

divide, replace, repeat until remainder 0

Last divisor = HCF.

HCF result

the last non-zero divisor

Not the 0 remainder.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Stopping Euclid's algorithm before the remainder is 0

✓ Keep dividing until the remainder is 0; the last divisor is the HCF.

WATCH OUT

✗ Taking the last remainder (0) as the HCF

✓ The HCF is the last non-zero divisor, not the 0 remainder.

WATCH OUT

✗ Ordering carelessly

✓ Use a clear rule (size or alphabetical) and check each item.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Ordering

Arrange numbers and names in order.

Questions

Euclid's algorithm

Find the HCF by repeated division.

Questions

Iterative processes

Describe and use repeating steps.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Ordering

Arrange in ascending order: 34, 12, 27, 8.

▶ Show solution

8, 12, 27, 34.

Q2MEDIUM· Euclid

Find the HCF of 48 and 18 using Euclid's algorithm.

▶ Show solution

48 = 18×2 + 12; 18 = 12×1 + 6; 12 = 6×2 + 0 → HCF = 6.

Q3MEDIUM· Euclid

Find the HCF of 36 and 24 by Euclid's algorithm.

▶ Show solution

36 = 24×1 + 12; 24 = 12×2 + 0 → HCF = 12.

Q4EASY· Concept

What is an iterative process?

▶ Show solution

A process that repeats the same step again and again until a condition is met.

Q5EASY· Ordering

Sort alphabetically: Asha, Ravi, Bala, Kavi.

▶ Show solution

Asha, Bala, Kavi, Ravi.

Q6MEDIUM· Euclid

Find the HCF of 60 and 48 by repeated division.

▶ Show solution

60 = 48×1 + 12; 48 = 12×4 + 0 → HCF = 12.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 3 Chapter 5 of Samacheer Kalvi Class 6 Maths.
•Arranging in order makes information easy to find and compare.
•An iterative process repeats the same step until a condition is met.
•Euclid's division algorithm: divide, replace, repeat until the remainder is 0.
•The HCF is the last non-zero divisor.
•Euclid's game is an iterative number game that also leads to the HCF.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 3-6 marks across ordering and algorithms

Question type	Marks each	Typical count	What it tests
Ordering	1	1-2	Arranging numbers/names
Euclid's algorithm	2	1-2	HCF by repeated division
Concept	1	1	Iterative process

Prep strategy

Choose a clear ordering rule
Repeat division until remainder 0
Take the last non-zero divisor as HCF
Recognise repeating steps as iteration

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Searching

Ordered lists (dictionaries, directories) are quick to search.

Computing

Algorithms like Euclid's are used in programming.

Problem solving

Iterative steps solve many maths problems.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

State the ordering rule used
Show each division step in Euclid's algorithm
Report the last non-zero divisor as the HCF
Identify the repeating step in iteration

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Find the HCF of 1071 and 462 using Euclid's algorithm.
Explain how Euclid's game decides a winner.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 6 Term 3 ExamMedium

Logical Reasoning / OlympiadMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

You divide the larger number by the smaller, then keep replacing the numbers with the divisor and remainder and dividing again, until the remainder is 0; the last divisor used is the HCF.

It repeats the same step over and over — each repetition is called an iteration — until some stopping condition is reached, like the remainder becoming 0.

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