Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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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

  1. What is Euler's totient function phi(12)?

    Answer: 4

    phi(12)=12*(1-1/2)*(1-1/3)=4.

  2. How many solutions does x^2 = 1 (mod 8) have among {0,1,2,...,7}?

    Answer: 4

    1^2=1, 3^2=9=1, 5^2=25=1, 7^2=49=1 (all mod 8), so there are 4 solutions.

  3. What is the largest prime factor of 2310?

    Answer: 11

    2310=2*3*5*7*11, so the largest prime factor is 11.

  4. How many trailing zeros does 50! end with?

    Answer: 12

    Trailing zeros equal the number of factors of 5: floor(50/5)+floor(50/25)=10+2=12.

  5. If n=2^3*3*5^2, how many ordered pairs (a,b) satisfy lcm(a,b)=n?

    Answer: 105

    For each prime power p^k, pairs with max exponent k number (2k+1); total=(7)(3)(5)=105.

  6. What is the remainder when 2^200 is divided by 3?

    Answer: 1

    2^(even)=1(mod3) since 2^2=1(mod3); 200 is even so remainder is 1.