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If a, b are two distinct prime number than a highest common factor of a, b is ___________  201ab

Question

If a, b are two distinct prime numbers then the highest common factor of a, b is ___________

201ab

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Solution

To solve for the highest common factor (HCF) of two distinct prime numbers a a and b b , we can follow these steps:

1. Break Down the Problem

  • Identify what is meant by the highest common factor.
  • Understand the properties of prime numbers.

2. Relevant Concepts

  • The HCF (also known as GCD, greatest common divisor) of two numbers is the largest positive integer that divides both numbers without leaving a remainder.
  • Prime numbers have exactly two distinct positive divisors: 1 and the number itself.

3. Analysis and Detail

  • Since a a and b b are distinct prime numbers,
    • The only common divisor they share is 1.
  • Therefore, the highest common factor of a a and b b is: HCF(a,b)=1 \text{HCF}(a, b) = 1

4. Verify and Summarize

  • For prime numbers a a and b b , the only factor they share is 1. Thus, we do not need to perform any additional calculations.

Final Answer

The highest common factor of a a and b b is 1 \mathbf{1} .

This problem has been solved

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