The Co-primes from the following pairs are ____.

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We are asked to find the pair which are co – primes from the given pairs.Let us check each and every Options one by one.(1) 7 and 63Now, let us use the prime factorisation for the number 7Here, we can see that the number 7 is a prime numberSo, we can take the prime factorisation for 7 as⇒7=1×7Now, let us use the prime factorisation method for 63 then we get

⇒63=
    3
    2
   
   ×7
  Here, we can see that there is common prime 7 in the prime factorisation of 7 and 63We know that the co – primes are the pair of numbers having only one common factor that is 1By using the above condition we can conclude that the pair 7 and 63 are not co – primes.(2) 36 and 25Now, let us use the prime factorisation method for 36 then we get

⇒36=
    2
    2
   
   ×
    3
    2

Now, let us use the prime factorisation method for 25 then we get

⇒25=
    5
    2

Here, we can see that there are no common factors for 36 and 25By using the co – primes definition we can conclude that the pair 36 and 25 are co – primes.(3) 35 and 21Now, let us use the prime factorisation method for 35 then we get⇒35=5×7Now, let us use the prime factorisation method for 21 then we get ⇒21=3×7Here, we can see that there is common factor for 35 and 21 that is 7By using the co – primes definition we can conclude that the pair 35 and 21 are not co – primes.(4) 63 and 81Now, let us use the prime factorization method for 63 then we get

⇒63=
    3
    2
   
   ×7
  Now, let us use the prime factorization method for 81 then we get

⇒81=
    3
    4

Here, we can see that there are no common factors for 63 and 81 that is 3By using the co – primes definition we can conclude that the pair 63 and 81 are not co – primes.

The Co-primes from the following pairs are ____.

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