The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2, the quotient is 33. Find the other number.
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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.