IMSA Number Theory and Arithmetic 1 — Questions and Answers
Question 1: What is the greatest common factor (GCF) of 36 and 48?
- 12 (Correct answer)
- 6
- 18
- 24
Correct answer: 12
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?
- 12 (Correct answer)
- 24
- 8
- 6
Correct answer: 12
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?
- 37 (Correct answer)
- 39
- 51
- 49
Correct answer: 37
37 is only divisible by 1 and itself, making it prime; the others have additional factors.
Question 4: What is 2³ × 3²?
- 72 (Correct answer)
- 18
- 36
- 54
Correct answer: 72
2³ = 8 and 3² = 9; 8 × 9 = 72.
Question 5: What is the prime factorization of 60?
- 2² × 3 × 5 (Correct answer)
- 2 × 3² × 5
- 2³ × 3 × 5
- 2 × 3 × 5²
Correct answer: 2² × 3 × 5
60 = 4 × 15 = 2² × 3 × 5.
Question 6: What is the value of 5! (5 factorial)?
- 120 (Correct answer)
- 60
- 24
- 20
Correct answer: 120
5! = 5 × 4 × 3 × 2 × 1 = 120.
IMSA Number Theory and Arithmetic 1
What is the greatest common factor (GCF) of 36 and 48?