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Problem 148

Algebra Difficulty 1.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2013

The value of $(2^3)^2 - 4^3$ is

Pick one

Official solution

The greatest common factor of two numbers is the largest positive integer which divides into both numbers with no remainder.

For answer (B), 50 divided by 20 leaves a remainder, so we may eliminate (B) as a possible answer.

Similarly for answer (D), 25 divided by 20 leaves a remainder, so we may eliminate (D) as a possible answer.

For answer (A), since 200 divides 200 and 200 divides 2000, the greatest common factor of 200 and 2000 cannot be 20.

For answer (E), since 40 divides 40 and 40 divides 80, the greatest common factor of 40 and 80 cannot be 20.
The largest positive integer which divides both 20 and 40 is 20, and so (C) is the correct answer.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.