Adv
Rajan@2021
  • 0
Guru

Use Euclid’s algorithm to find HCF of 1190 and 1445. Express the HCF in the form of 1190m+1445n.

  • 0

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

Share

1 Answer

  1. 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

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions