Track / Stage 4 / 330 of 340 #590 of 1964

Problem 590

AMC 12 late, AIME early

Number theory Difficulty 5.0 Find the answer

Variant 10.1.1. (a) (2 points) A natural number $n$ is less than 120. What is the largest remainder that the number 209 can give when divided by $n$ ?

(b) (2 points) A natural number $n$ is less than 90. What is the largest remainder that the number 209 can give when divided by $n$ ?

Your answer

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

Official solution

Answer: (a) 104. (b) 69.

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