IMO Number Theory 1 — Questions and Answers
Question 1: Which of the following numbers is a prime number?
- 21
- 27
- 29 (Correct answer)
- 33
Correct answer: 29
29 is prime because it has no divisors other than 1 and itself.
Question 2: What is the LCM of 4 and 6?
- 10
- 12 (Correct answer)
- 24
- 48
Correct answer: 12
The Least Common Multiple of 4 and 6 is 12, the smallest number both divide evenly.
Question 3: What is the HCF (GCD) of 18 and 24?
- 3
- 4
- 6 (Correct answer)
- 9
Correct answer: 6
The Highest Common Factor of 18 and 24 is 6, as 6 is the largest number that divides both.
Question 4: Which of the following is a composite number?
- 2
- 7
- 11
- 15 (Correct answer)
Correct answer: 15
15 = 3 × 5, so it is composite because it has factors other than 1 and itself.
Question 5: What are the prime factors of 36?
- 2 and 3 (Correct answer)
- 3 and 4
- 2, 3, and 6
- 4 and 9
Correct answer: 2 and 3
36 = 2² × 3², so its prime factors are 2 and 3.
Question 6: Which of the following numbers is divisible by both 3 and 4?
- 18
- 20
- 24 (Correct answer)
- 30
Correct answer: 24
24 ÷ 3 = 8 and 24 ÷ 4 = 6, so 24 is divisible by both 3 and 4.
IMO Number Theory 1
Which of the following numbers is a prime number?