Innings2
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Playing With Numbers

    Introduction

    Factors and Multiples

    Prime and Composite Numbers

    Even and Odd numbers

    Tests for Divisibility of Numbers

    Prime Factorisation

    Common Factors and Common Multiples

    Exercise 3.1

    Exercise 3.2

    Exercise 3.3

    Exercise 3.4

    Exercise 3.5

    Exercise 3.6

    Exercise 3.7

    What Have We Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

    Enhanced Curriculum Support

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…

Playing With Numbers > What Have We Discussed?

What Have We Discussed?

  1. We have discussed multiples, divisors, factors and have seen how to identify factors and multiples.

  2. We have discussed the following:

(i) A of a number is an exact divisor of that number.

(ii) Every number is a factor of itself. is a factor of every number.

(iii) Every factor of a number is less than or to the given number.

(iv) Every number is a of each of its factors.

(v) Every multiple of a given number is than or equal to that number.

(vi) Every number is a of itself.

  1. We have learnt that:

(i) The number other than 1, with only factors namely 1 and the number itself, is a number. Numbers that have more than two factors are called numbers. Number is neither prime nor composite.

(ii) The number 2 is the smallest number and is . Every prime number other than 2 is .

(iii) Two numbers with only as a common factor are called co-prime numbers.

(iv) If a number is divisible by another number, then it is divisible by each of the factors of that number.

(v) A number divisible by two co-prime numbers is divisible by their also.

  1. We have discussed how we can find just by looking at a number, whether it is divisible by small numbers 2, 3, 4, 5, 8, 9 and 11. We have explored the relationship between digits of the numbers and their divisibility by different numbers.

(i) Divisibility by 2, 5 and 10 can be seen by just the digit.

(ii) Divisibility by 3 and 9 is checked by finding the of digits.

(iii) Divisibility by 4 and 8 is checked by the last and digits respectively.

(iv) Divisibility of 11 is checked by comparing the of digits at odd and even places.

  1. We have discovered that if two numbers are divisible by a number then their sum and difference are also divisible by that number.

  2. We have learnt that:

(i) The Highest Common Factor (HCF) of two or more given numbers is the of their common factors.

(ii) The Lowest Common Multiple (LCM) of two or more given numbers is the of their common multiples.

  1. If one of the two given numbers is a multiple of the other, then the greater number will be their .

  2. Relationship between LCM and HCF: LCM × HCF = of the two numbers.