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Number Theory

Divisibility, mods, primes.

Number TheoryDivisibility★☆☆☆☆Easy+20 XP

What is the remainder when 24 is divided by 5?

Number TheoryGCD/LCM★☆☆☆☆Easy+20 XP

What is the greatest common divisor of 18 and 24?

Number TheoryGCD/LCM★☆☆☆☆Easy+20 XP

What is the least common multiple of 6 and 8?

Number TheoryPrimes★★☆☆☆Medium+30 XP

How many prime numbers are less than 20?

Number TheoryDivisibility★★☆☆☆Medium+30 XP

What is the sum of the digits of 5⁴?

Number TheoryDivisibility★★☆☆☆Medium+30 XP

How many positive divisors does 36 have?

Number TheoryDivisibility★★☆☆☆Medium+30 XP

What is 2¹⁰?

Number TheoryModular arithmetic★★☆☆☆Medium+30 XP

What is the remainder when 7³ is divided by 5?

Number TheoryGCD/LCM★★☆☆☆Medium+30 XP

What is the smallest integer greater than 50 that is divisible by both 4 and 6?

Number TheoryModular arithmetic★★★☆☆Hard+40 XP

What is the units digit of 3²⁰²⁶?

Number TheoryModular arithmetic★★★☆☆Hard+40 XP

What is the remainder when 2¹⁰ is divided by 7?

Number TheoryDivisibility★★★☆☆Hard+40 XP

How many positive divisors does 360 have?

Number TheoryDivisibility★★★☆☆Hard+40 XP

What is the sum of all positive divisors of 28?

Number TheoryModular arithmetic★★★☆☆Hard+40 XP

What is the remainder when 7⁴ is divided by 100?

Number TheoryDiophantine equations★★★☆☆Hard+40 XP

What is the smallest positive integer n with n ≡ 2 (mod 3) and n ≡ 3 (mod 5)?

Number TheoryDivisibility★★★★☆Expert+55 XP

How many trailing zeros does 100! have?

Premium problem

How many positive integers less than 36 are relatively prime to 36? (This is φ(36).)

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Premium problem

What is the largest exponent k such that 3^k divides 50!?

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Premium problem

What is gcd(2¹² − 1, 2⁸ − 1)?

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