This is the basic and conceptual question from real numbers in which we have given two numbers 320 and 457 and we have been asked to find the largest number which divides the above number leaving remainders 5 and 7 respectively.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 1B, question no 9
The largest number which divides 320 and 457 leaving remainders5 and 7 respectively
= HCF of (320−5) and (457−7)
= HCF of 315 and 450
450=315×1+135
315=135×2+45
135=45×3+0
∴ HCF of 450 and 315 is 45.
So, the largest number which divides 320 and 457 leaving remainders 5 and 7 respectively is 45.