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 the sum of all positive divisors of 28?

    Answer: 56

    28=2^2*7; sum of divisors=(1+2+4)(1+7)=7*8=56.

  2. How many two-digit prime numbers exist?

    Answer: 21

    There are 21 primes between 11 and 97: 11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

  3. What is lcm(12, 18)?

    Answer: 36

    lcm(12,18)=12*18/gcd(12,18)=216/6=36.

  4. For which prime p is p^2+2 also prime?

    Answer: 3

    p=3 gives 9+2=11 (prime); all primes p>3 give p^2=1(mod3) making p^2+2=0(mod3).

  5. What is the units digit of 7^53?

    Answer: 7

    Units digits of powers of 7 cycle as 7,9,3,1 with period 4; 53=1(mod4), so units digit is 7.

  6. How many perfect squares are strictly between 100 and 400?

    Answer: 9

    From 11^2=121 to 19^2=361, there are 19-11+1=9 perfect squares.