Curriculum · Number Theory · Divisibility & Primes

Number Bases & Digits

Base-b representation, digit sums, and divisibility rules that fall out of them.

Objectives

Convert between bases
Prove divisibility rules
Solve digit puzzles

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Divisibility & Primes mastery now.

Train the topic

●●○○○How many positive divisors does

36

have?AMC 8 style ●●○○○What is

\gcd(84, 126)

?AMC 8 style ●●●○○What is the smallest positive integer with exactly

6

divisors?AMC 10 style ●●●○○Two positive integers have

\gcd = 6

and

\text{lcm} = 180

. If one of them is

36

, what is the other?AMC 10 style ●●●○○In how many zeros does

25!

end?AMC 10 style