# CAT Quantitative Aptitude Questions | CAT Number Systems - HCF and LCM questions

###### CAT Questions | Number Theory | HCF basics CAT Questions

The question is about HCF basics. Given the sum of two numbers, we need to find out the maximum possible HCF between those values. A range of CAT questions can be asked based on this simple concept.In CAT Exam, one can generally expect to get 1~2 questions from CAT Number Systems: HCF and LCM. In multiple places, extension of HCF and LCM concepts are tested by CAT Exam and one needs to understand HCF and LCM to be able to answer the same. CAT Number theory is an important topic with lots of weightage in the CAT Exam.

Question 6: Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?

1. 350
2. 700
3. 1050
4. 525

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##### Method of solving this CAT Question from Number Theory - HCF and LCM: Having been given sum of two numbers, what inferences can we draw about the HCF of the two numbers. Can we draw any inference at all?

x = 525 and y = 525 works best.

If the question states x, y have to be distinct, then the best solution would be x = 350, y = 700, HCF = 350.

So the HCF is 525.

The question is "What is the maximum value of the HCF between x and y?"

##### Hence the answer is "525"

Choice D is the correct answer.

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