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Problem 339

AMC 12 late, AIME early

Number theory Difficulty 4.7 Find the answer

145. Find two numbers if their sum is 432, and their greatest common divisor is 36.

Your answer

Official solution

145. Given $x=36 x_{1}$ and $y=36 y_{1}$ , and $\left(x_{1}, y_{1}\right)=$ $=1$ . We find $x_{1}+y_{1}=12$ , hence $x_{1}=1, y_{1}=11 ; x_{2}=$ $=5, y_{2}=7$ .

Answer. $x_{1}=36, y_{1}=396 ; x_{2}=180, y_{2}=252$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.