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Let’s assume that the two numbers are A and B.

We know that the HCF of A and B is 33. Therefore, we can write:

A = 33x B = 33y

where x and y are co-prime integers (i.e., they have no common factors other than 1).

We also know that the LCM of A and B is 264. Therefore, we can write:

LCM(A, B) = 264

Multiplying the values of A and B that we obtained above, we get:

A x B = (33x) x (33y) = 1089xy

Therefore, we can write:

LCM(A, B) = 264 = (HCF(A, B)) x (A/B) x B

Substituting the values of HCF(A, B) and A/B from the problem statement, we get:

264 = 33 x 33 x B/33

Simplifying, we get:

264 = 33B

B = 8

Substituting this value of B in the equation A x B = 1089xy, we get:

A x 8 = 1089xy

Substituting the value of A/B = 33, we get:

A = 33 x 8 = 264

Therefore, the two numbers are A = 264 and B = 8.