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CHAPTER – 3 | PLAYING WITH NUMBERS 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. (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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