Find hcf of 210 and 55 and express as a linear combination

Question

Arun · Answer

HCF of 210 & 55 210 = 55* 3 + 45 ….....(i) 55 = 45 * 1 +10 ….........(ii) 45 = 10 *4 +5 …...........(iii) 10 = 5 *2 + 0 hence HCF of 210 & 55 = 5 now from (iii), we get 4 5 = 10 *4 + 5 so 5 = 45 – 10*4 5 = 45 – (55 – 45)*4 5 = 45 – 55*4 + 45*4 5 = 45 *5 – 55*4 5 = (210 – 55*3) *5 – 55*4 5 = 210*5 – 55*15 – 55*4 5 = 210*5 – 55*19 5 = 210 x + 55 y where x = 5, y = –19 hope it helps

Kushagra Madhukar · Answer

Dear student, Please find the attached solution to your question. HCF of 210 & 55 210 = 55* 3 + 45 ….....(i) 55 = 45 * 1 +10 ….........(ii) 45 = 10 *4 +5 …...........(iii) 10 = 5 *2 + 0 Hence HCF of 210 & 55 = 5 now from (iii), we get 45 = 10 *4 + 5 so, 5 = 45 – 10*4 5 = 45 – (55 – 45)*4 5 = 45 – 55*4 + 45*4 5 = 45 *5 – 55*4 5 = (210 – 55*3) *5 – 55*4 5 = 210*5 – 55*15 – 55*4 5 = 210*5 – 55*19 5 = 210 x + 55 y where x = 5, y = –19 Hope it helps. Thanks and regards, Kushagra

RISHIKA · Answer

HI FRIENDS

Firstly we will find the hcf of 55 and 210 by applying Euclid's division algorithm
210>55
*210=55x3+45........(1)
*55=45x1+10.......(2)
*45=10x4+5..........(3)
*10=5x2+0..........(4)
so, HCF is 5
from equation 3 we have
5=45-(10x4)

5 = 45 – (55 – 45)*4. ( from equation 2)

5 = 45 – 55*4 + 45*4

5 = 45 *5 – 55*4

5 = (210 – 55*3) *5 – 55*4

5 = 210*5 – 55*15 – 55*4

5 = 210*5 – 55*19

5 = 210a + 55b

where a = 5

b=-19

thanks

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Find hcf of 210 and 55 and express as a linear combination

Find hcf of 210 and 55 and express as a linear combination

3 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on 10 grade maths

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship