MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers
Problem
Let the positive integers be 1672 and 1053.
(i) Find the HCF of 1672 and 1053, showing every step of your working.
(ii) Using the successive remainders obtained in part (i), express the HCF as a linear combination of 1672 and 1053, that is, in the form 1672x+1053y where x and y are integers.
(iii) Explain how the result in part (ii) confirms that the integer you found in part (i) is indeed the greatest common divisor of 1672 and 1053.