This is the basic and conceptual question from real numbers in which we have given two numbers 1190 and 1445 and we have to find the HCF by using the method of Euclid’s algorithm and we have to express the HCF in the form of 1190m+1445n.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 1A, question no 10
Here 1145 > 1190
Use Euclid’s algorithm
1445 =1190 x 1 + 255
1190 = 255 x 4 +170
255 = 170 x 1 + 85
170 = 85 x 2 + 0
Remainder is zero. Stop the process. This implies, HCF = 85
Now, Express the HCF in the form 1190m + 1445n.
85 = 255 – 170
= (1445 – 1190) – (1190 – 255 x 4)
= 1445 – 1190 – 1190 + 255 x 4
= 1445 – 1190 x 2 + 1445 x 4 – 1190 x 4
= 1445 x 5 – 1190 x 6
= 1190 x (-6) + 1445 x 5
choose m = -6 and n = 5
= 1190 m + 1445 n