Something's wrong!  35 is NOT a factor of 77, so it cannot be the 
the HCF of 77 and any other number since it's not even a factor of 77.
If your teacher gave you 77, you must point it out to him/her that
35 is not a factor of 77, thus 35 cannot be the HCF of it and any 
other positive integer. 
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But I won't leave you hanging:

Here is a similar problem that makes sense:

The HCF and LCM of two positive integers are 12 and 5544 respectively.
If one of the integers is 264, what is the other integer.

We know that 264, 5544, and the unknown integer are all multiples of 12.

We divide 5544 by 12, getting 462, which contains all the prime factors of 
5544 as many times as and no more than they are contained in both 264 and the
unknown integer.

We divide 264 by 12, getting 22, which must contain all but only those
prime factors of 5544 that are contained in 264 but not in the unknown
integer. 

We reason:
462 must contains all the prime factors of the unknown integer that
22 does not contain as prime factors.

So we divide 462 by 22, getting 21, which contains all those,
and only those, factors of 12 that 264 does not contain.

Therefore the unknown integer has to be a multiple of
as those factors of 5544 which 264 does not contain, so it
must be 21*12 = 252

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Here is a formula for this kind of problem:

The HCF and LCM of two positive
integers are H and L respectively.
If one of the integers is A, what is
the other integer B?

B = [(L÷H)÷(A÷H)]H

If you have any questions, feel free to ask them in the 
thank-you note form below.

Edwin