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smc

number theory intermediate

Problem

If the Highest Common Divisor of

6432

and

132

is diminished by

8

, it will equal:

(A)

- 6

(B)

6

(C)

- 2

(D)

3

(E)

4

Solution

g cd (6432, 132)

13 \cdot 12 = 132

\frac{6432}{6} = 1072 ⟹ \frac{1072}{4} = 268 ⟹ \frac{268}{4} = 67

, so

g cd (2^{5} \cdot 3 \cdot 67, 2^{2} \cdot 3 \cdot 13) = 2^{2} \cdot 3 = 12 ⟹ 12 - 8 = 4, 4

Final answer

E