UTMA Number Theory and Arithmetic

Question 1

What is the greatest common divisor (GCD) of 84 and 126?

Accepted Answer

42

Answer

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?

Accepted Answer

97

Answer

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?

Accepted Answer

72

Answer

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?

Accepted Answer

6

Answer

If n ≡ 3 (mod 7), then 2n ≡ 6 (mod 7).

Question 5

How many positive divisors does 360 have?

Accepted Answer

24

Answer

360 = 2³ × 3² × 5¹, so the number of divisors is (3+1)(2+1)(1+1) = 24.

UTMA - University of Toronto Math Assessment Practice Test