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Number Theory Basics

Primes, factors, GCD/LCM, and more.

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Vanessa is throwing a party for at least 3 other friends and buys a bag of 546 pieces of candy. At the party, they evenly distribute the candies among all people. If the number of people present is odd, what is the smallest number of people that could be present?

You are trying to buy either 100 candy bars or 60 ice cream sandwiches for a group of \(n\) friends (\(n\) includes yourself). With either choice, you would be able to split the treats equally among your \(n\) friends. What is the largest possible value of \(n\)?

Suppose Alice has 10 apples and wants to share them equally amongst herself and her \(n\) friends so that everyone gets the same number of apples. If Alice has at least 1 friend, how many \(n\) are there such that Alice could have \(n\) friends?

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