AMC 8 Number Theory & Divisibility 1 — Questions and Answers
Question 1: What is the greatest common factor (GCF) of 48 and 36?
- 6
- 9
- 12 (Correct answer)
- 18
Correct answer: 12
The GCF of 48 and 36 is 12, since 12 divides both and no larger number does.
Question 2: Which of the following is a prime number?
- 51
- 57
- 61 (Correct answer)
- 63
Correct answer: 61
61 is prime because it has no factors other than 1 and itself.
Question 3: What is the least common multiple (LCM) of 6 and 8?
- 12
- 16
- 24 (Correct answer)
- 48
Correct answer: 24
The LCM of 6 and 8 is 24, the smallest positive number divisible by both.
Question 4: How many positive factors does 36 have?
- 6
- 7
- 8
- 9 (Correct answer)
Correct answer: 9
36 = 2² × 3² has (2+1)(2+1) = 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Question 5: What is the sum of all positive factors of 12?
- 24
- 28 (Correct answer)
- 30
- 32
Correct answer: 28
The factors of 12 are 1, 2, 3, 4, 6, 12, and 1+2+3+4+6+12 = 28.
Question 6: If a number leaves a remainder of 3 when divided by 7, what remainder does twice that number leave when divided by 7?
- 3
- 5
- 6 (Correct answer)
- 1
Correct answer: 6
If n ≡ 3 (mod 7), then 2n ≡ 6 (mod 7).
AMC 8 Number Theory & Divisibility 1
What is the greatest common factor (GCF) of 48 and 36?