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a)a

b)ab

c)b

d)1

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Hint: A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers (both greater than1) or a number which has only two factors ‘1’ and the number itself termed as prime number. HCF stands for highest common factor, it means the greatest number which divides given two or more numbers is termed as H.C.F of them. Use these definitions to solve the problem.

Complete step by step answer:

As we know HCF stands for highest common factor means the greatest common divisor of two or more integers which are not all zero, i.e. the highest number which divides all of the given numbers is called as H.C.F. of them.

And we know the definition of a prime number as well. It is a natural number (counting number = 1, 2, 3, 4, …………….. ) greater than 1 that is not a product of two smaller natural numbers (both greater than 1) or a number which has only two factors (divisors), one factor is ‘1’ and other is the number itself is called as a prime number.

It means any two prime numbers will have only one common factor and that would be ‘1’, as per the definitions of prime number and highest common factor. Hence, any two different prime numbers will have the highest common factor as ‘1’. It means the H.C.F. of given two prime numbers a and b is 1. Hence, option d is the correct answer.

Note: Use the fundamental definitions and concepts of both. Examples related to the question can be given as: Find the H.C.F. of 7 and 11. As factors of 7 and 11 are (1, 7) and (1, 11) respectively. So, the only factor common to both is 1. So, ‘1’ is the H.C.F. of them.

Don’t confuse the definitions of H.C.F. and L.C.M as L.C.M is a multiple and H.C.F is a factor. One may go wrong if he/she gives the answer as ‘ab’, because it is representing the L.C.M of a and ‘b’ not H.C.F. so, take care and be clear with both H.C.F and L.C.M.

Complete step by step answer:

As we know HCF stands for highest common factor means the greatest common divisor of two or more integers which are not all zero, i.e. the highest number which divides all of the given numbers is called as H.C.F. of them.

And we know the definition of a prime number as well. It is a natural number (counting number = 1, 2, 3, 4, …………….. ) greater than 1 that is not a product of two smaller natural numbers (both greater than 1) or a number which has only two factors (divisors), one factor is ‘1’ and other is the number itself is called as a prime number.

It means any two prime numbers will have only one common factor and that would be ‘1’, as per the definitions of prime number and highest common factor. Hence, any two different prime numbers will have the highest common factor as ‘1’. It means the H.C.F. of given two prime numbers a and b is 1. Hence, option d is the correct answer.

Note: Use the fundamental definitions and concepts of both. Examples related to the question can be given as: Find the H.C.F. of 7 and 11. As factors of 7 and 11 are (1, 7) and (1, 11) respectively. So, the only factor common to both is 1. So, ‘1’ is the H.C.F. of them.

Don’t confuse the definitions of H.C.F. and L.C.M as L.C.M is a multiple and H.C.F is a factor. One may go wrong if he/she gives the answer as ‘ab’, because it is representing the L.C.M of a and ‘b’ not H.C.F. so, take care and be clear with both H.C.F and L.C.M.