Track / Stage 4 / 187 of 340 #447 of 1964

Problem 447

AMC 12 late, AIME early

Number theory Difficulty 4.8 Find the answer

A natural number, its 2 times has exactly 2 more factors than it has, and its 3 times has exactly 3 more factors than it has. This natural number is $\qquad$ .

Your answer

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

Official solution

answer: 12

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.