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Rajan@2021
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Using Euclid’s division algorithm, find the HCF of 960 and 1575.

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We have been asked to find the HCF of the numbers 960 and 1575 by using the method of Euclid’s Division algorithm.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1A, question no 4(iii)

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  1. (iii) Step 1: Choose bigger number : 1575>960

    On dividing 1575 by 90 , we have
    quotient = 1 remainder = 615
    1575=960×1+615

    Step 2 : on Dividing 960 by 615 , we have

    Quotient = 1 and remainder =345
    960=615×1+345

    Step 3 :on dividing 615 by 345
    quotient 1 and remainder = 270

    615=345×1+270

    Step 4 : On dividing 345 by 270 , we have

    quotient = 1 and rem,ainder = 75
    345=270×1+75

    Step 5 : dividing 270 by 75 , we get
    Quotient= 3, remainder = 30
    270=75×+45

    Step 6 : Dividing 75 by 45 we get

    Quotient = 1, remainder = 30

    75=45×1+30

    Step 7: Dividing 45 by 30 , we get

    quotient = 1and remainder = 15

    45=30×1+15

    Step 8 :  Dividing 30  y 15 , we get

    quotient = 2 and remainder = 0

    Since remainder is zero, stop the process

    Therefore , HCF of 1575 and 960 is 15.

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