HMMT February

Number theory Difficulty 4.8 AIME Find the answer

A product of five primes is of the form $A B C, A B C$ , where $A, B$ , and $C$ represent digits. If one of the primes is 491, find the product $A B C, A B C$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$491 \cdot 1001 \cdot 2=982,982$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.