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In this, simply use the concept of prime number and their theoretical concept that a number which is not divisible with the other number can be divisible with a new number.

Since, it is known thatif a, b and b, c are co-primes, then a, c may not be co-primes. This is because a number which is not divisible with the other number, could be divisible with a new number.

To prove this, Let鈥檚 take an example which proves this situation,

Assume:$a=16,b=35,c=64$

For a and b :-

Now, finding the factor of 16:$16=1,2,4,8,16$

The factor of 35 : $35=1,5,7,35$

The greatest common factor is 1.

For b and c :-

The factor of 35 :$35=1,5,7,35$

The factor of 64 :$64=1,2,4,8,16,32,64$

The greatest common factor is 1 .

For a and c :-

the factor of 16 :$16=1,2,4,8,16$

The factor of 64 :$64=1,2,4,8,16,32,64$

The GCF is 16.

Hence, it is clearly seen from the above that the factor of a and c be different from a and b, b and c.