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COMC Number Theory and Algebra Flashcards

6 cards from real COMC practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 COMC Number Theory and Algebra flashcards as text

  1. What is the sum of all positive divisors of 28?

    Answer: 56

    The divisors of 28 are 1, 2, 4, 7, 14, and 28, which sum to 56.

  2. What is the remainder when 7^100 is divided by 4?

    Answer: 1

    Since 7 ≡ 3 (mod 4) and 3² ≡ 1 (mod 4), we get 7^100 ≡ (3²)^50 ≡ 1 (mod 4).

  3. How many positive divisors does 360 have?

    Answer: 24

    Since 360 = 2³ × 3² × 5¹, the divisor count is (3+1)(2+1)(1+1) = 24.

  4. If gcd(a, b) = 6 and lcm(a, b) = 60, what is the product ab?

    Answer: 360

    For any positive integers, gcd(a,b) × lcm(a,b) = ab, so ab = 6 × 60 = 360.

  5. What is the smallest positive integer that has exactly 5 positive divisors?

    Answer: 16

    A number with exactly 5 divisors must be p^4 for a prime p; the smallest is 2^4 = 16.

  6. What is the remainder when 2026² is divided by 10?

    Answer: 6

    The last digit of 2026 is 6, and 6 raised to any positive power always ends in 6, so the remainder is 6.