1954 AHSME Problems/Problem 4

Problem 4

If the Highest Common Divisor of $6432$ and $132$ is diminished by $8$ , it will equal:

$\textbf{(A)}\ -6 \qquad \textbf{(B)}\ 6 \qquad \textbf{(C)}\ -2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution

$\gcd(6432, 132)$ $13\cdot 12=132$ $\frac{6432}{6}=1072\implies\frac{1072}{4}=268\implies\frac{268}{4}=67$ , so $\gcd(2^5\cdot 3\cdot 67, 2^2\cdot 3\cdot 13)=2^2\cdot 3=12\implies 12-8=4, \fbox{E}$

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1954 AHSME Problems/Problem 4

Problem 4

Solution