Number Theory Flashcards
6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Number Theory flashcards as text
What is the remainder when 7^100 is divided by 5?
Answer: 1
7=2(mod5); powers of 2 mod 5 cycle as 2,4,3,1 with period 4; since 100=0(mod4), remainder is 1.
How many positive divisors does 360 have?
Answer: 24
360=2^3*3^2*5, so the number of divisors is (3+1)(2+1)(1+1)=24.
What is gcd(48, 36)?
Answer: 12
48=36*1+12 and 36=12*3+0, so gcd=12.
What is the smallest positive integer with exactly 6 divisors?
Answer: 12
12=2^2*3 has (2+1)(1+1)=6 divisors, and no smaller positive integer has exactly 6.
How many integers from 1 to 100 are divisible by 3 or 5?
Answer: 47
By inclusion-exclusion: 33+20-6=47.
What is 13^2 mod 7?
Answer: 1
13=-1(mod7), so 13^2=(-1)^2=1(mod7).