IMSA Number Theory and Arithmetic

Question 1

What is the greatest common factor (GCF) of 36 and 48?

Accepted Answer

12

Answer

The factors of 36 are 1,2,3,4,6,9,12,18,36 and of 48 are 1,2,3,4,6,8,12,16,24,48; the greatest common factor is 12.

Question 2

What is the least common multiple (LCM) of 4 and 6?

Accepted Answer

12

Answer

Multiples of 4: 4,8,12; multiples of 6: 6,12; the LCM is 12.

Question 3

Which of the following is a prime number?

Accepted Answer

37

Answer

37 is only divisible by 1 and itself, making it prime; the others have additional factors.

Question 4

What is 2³ × 3²?

Accepted Answer

72

Answer

2³ = 8 and 3² = 9; 8 × 9 = 72.

Question 5

What is the prime factorization of 60?

Accepted Answer

2² × 3 × 5

Answer

60 = 4 × 15 = 2² × 3 × 5.

IMSA - Intermediate Math Skill Assesment Practice Test