## Pre-Requisires

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**PLAYING WITH NUMBERS | Speed Notes**

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We have discussed multiples, divisors, factors and have seenhow to identify factors and multiples. We have discussed and discovered thefollowing: **(a) **A factor of a number is an exactdivisor of thatnumber. **(Scroll down to continue …)**

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**(b) **Every number is a factor of itself. 1 is a factor ofevery number.

**(c) **Every factor ofa number isless than or equal tothe given number.

**(d) **Every number isa multiple ofeach of itsfactors.

**(e) **Every multiple ofa given number is greater thanor equal tothat number.

**(f) **Every number is a multiple of itself.

We have learnt that – **(a) **The number otherthan 1, withonly factors namely 1 and thenumber itself, isa prime number. Numbers that have more than two factors are called composite numbers. Number 1is neither prime nor composite.

**(b) **The number 2is the smallest prime number andis even. Every prime number other than 2 isodd.

**(c) **Two numbers withonly 1 asa common factor are called co-prime numbers.

**(d) **If a number is divisible byanother number thenit is divisible by each of the factors of that number.

**(e) **A number divisible by two co-prime numbers is divisible by their product also.

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 thenumbers and theirdivisibility by different numbers.

**(a) **Divisibility by 2,5and 10 canbe seen byjust the lastdigit.

**(b) **Divisibility by 3and 9 ischecked by finding the sum ofall digits.

**(c) **Divisibility by 4 and 8is checked bythe last 2and 3 digits respectively.

**(d) **Divisibility of11 is checked by comparing thesum of digits at odd andeven places.

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

We have learnt that – **(a) **The Highest Common Factor (HCF) of two ormore given numbers is the highest of their common factors.

**(b) **The Lowest Common Multiple (LCM) of two ormore given numbers is the lowest of their common multiples.

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