Track / Stage 1 / 234 of 240 #234 of 2444

Problem 234

Number theory Difficulty 1.7 Multiple choice CEMC Gauss (Grade 8) · Canada · 2024

The prime factorization of $\$6\times 5\times 4\times 3\times 2\times$ 1$ can be written in the form
$2^a \times 3^b \times 5^c$ . The
value of $a+b+c$ is

Pick one

Official solution

Expressing the product $6\times5\times4\times3\times2\times1$ in
terms of prime factors, we get $6\times5\times4\times3\times2\times1=(2\times3)\times5\times(2\times2)\times3\times2$ This
product has $4$ factors of $2$ , $2$
factors of $3$ , and $1$ factor of $5$ , and thus is equal to $2^4\times3^2\times5^1$ .

The value of $a+b+c$ is $4+2+1=7$ .

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