Question

hcf of two or more prime numbers is always​

Answer 1

Answer:

A prime number is the number which has only two factors,1 and the number itself. hence 1 is only common factor fir two prime numbers making it HCF.

Answer 2

Consider two prime numbers x and y. The only divisors of x are 1 and x. Similarly, for y its only divisors are 1 and y. Since x#y, and both are different prime numbers , they have no common factor other than 1.

As example consider the prime numbers 5 and 37 . The factors/divisors of 5 are 1,5 and nothing else. The divisors of 37 are 1, 37 and no other number. Now H.C.F. , the Highest Common Factor is the Highest of all the factors that are common to both 5 and 37. Since 1 is the only common factor of 5 and 37, it follows that the highest common factor or HCF of 5 and 37 is 1.

The above logic applies to all numbers because prime numbers are only for positive integers.

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