UTMA Number Theory and Arithmetic 1 — Questions and Answers
Question 1: What is the greatest common divisor (GCD) of 84 and 126?
- 21
- 42 (Correct answer)
- 14
- 63
Correct answer: 42
Using the Euclidean algorithm: 126 = 1×84 + 42, then 84 = 2×42 + 0, so GCD = 42.
Question 2: Which of the following is a prime number?
- 91
- 87
- 97 (Correct answer)
- 93
Correct answer: 97
97 has no divisors other than 1 and itself, making it prime; 91 = 7×13, 87 = 3×29, 93 = 3×31.
Question 3: What is the least common multiple (LCM) of 12, 18, and 24?
- 36
- 48
- 72 (Correct answer)
- 144
Correct answer: 72
Prime factorizations give LCM = 2³ × 3² = 72.
Question 4: If a number leaves a remainder of 3 when divided by 7, what is the remainder when twice that number is divided by 7?
- 1
- 6 (Correct answer)
- 3
- 5
Correct answer: 6
If n ≡ 3 (mod 7), then 2n ≡ 6 (mod 7).
Question 5: How many positive divisors does 360 have?
- 18
- 20
- 24 (Correct answer)
- 30
Correct answer: 24
360 = 2³ × 3² × 5¹, so the number of divisors is (3+1)(2+1)(1+1) = 24.
Question 6: What is 2⁰ + 2¹ + 2² + 2³ + 2⁴?
- 28
- 30
- 31 (Correct answer)
- 32
Correct answer: 31
1 + 2 + 4 + 8 + 16 = 31, which equals 2⁵ − 1.
UTMA Number Theory and Arithmetic 1
What is the greatest common divisor (GCD) of 84 and 126?