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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(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.