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CISCEICSE ICSE Class 6
Textbook Solutions9522
Concept Notes & Videos307
Syllabus

Finding Factors Using Rectangular Arrangements and Division

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Topics

  • Introduction
  • Finding Factors Using Rectangular Arrangements
  • Finding Factors Using Division
  • Real-Life Example
  • Key Points Summary
CISCE: Class 6

Introduction

Imagine you have 12 desks to arrange in your classroom. How many different ways can you arrange them so that each row has the same number of desks and no desk is left unused? Each arrangement gives you a clue about the divisors (factors) of 12.

CISCE: Class 6

Finding Factors Using Rectangular Arrangements

1. For 2 coins

Example:

  • 1 × 2
  • 2 × 1
  • Factors of 2: 1, 2.

2. For 4 coins
 
Example:

  • 1 × 4
  • 2 × 2
  • 4 × 1
  • Factors of 4: 1, 2, 4.

3. For 6 coins

Example:

  • 1 × 6
  • 2 × 3
  • 3 × 2
  • 6 × 1
  • Factors of 6: 1, 2, 3, 6.
CISCE: Class 6

Finding Factors Using Division

If the remainder = 0, it's a factor.

  1. On dividing 6 by 1, we get a quotient = 6 and a remainder = 0. 
    `1")"overline(6)"("6`
      - 6  
        0
  2. On dividing 6 by 2, we get Quotient = 3 and Remainder = 0. 
    `2")"overline(6)"("3`
      - 6  
        0
  3. On dividing 6 by 3, we get Quotient = 2 and Remainder = 0. 
    `3")"overline(6)"("2`
      - 6  
        0
  4. On dividing 6 by 4, we get Quotient = 1 and Remainder = 2. 
    `4")"overline(6)"("1`
      - 6  
        2
  5. On dividing 6 by 5, we get Quotient = 1 and Remainder = 1. 
    `5")"overline(6)"("1`
      - 5  
        1
  6.  On dividing 6 by 6, we get Quotient = 1 and Remainder = 0. 
    `6")"overline(6)"("1`
      - 6  
        0

Here, we see that 1, 2, 3, and 6 are exact divisors of 6 and are called factors of 6. 
Therefore, factors of 6 = 1, 2, 3, 6

CISCE: Class 6

Real-Life Example

You want to put them in boxes so that each box has the same number of chocolates, without any leftover.

  • 1 box of 12

  • 2 boxes of 6

  • 3 boxes of 4

  • 4 boxes of 3

  • 6 boxes of 2

  • 12 boxes of 1

Each arrangement demonstrates a factor pair of 12.

CISCE: Class 6

Key Points Summary

  • A factor divides a number exactly (no remainder).

  • Rectangular arrangements represent all possible factor pairs.

  • Factors always come in pairs (row × column).

  • You can use division to check if a number is a factor.

Test Yourself

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