Number Theory questions – LCM HCF

Here are a few questions from LCM & HCF?

1. How many pairs of positive integers x,y exist such that HCF of, x,y = 35 and sum of x and y = 1085?

2. How many pairs of positive integers x,y exist such that HCF(x,y) + LCM (x,y) = 91?

3. Sum of two numbers x,y = 1050. What is the maximum value of the HCF between x and y?

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