College Math Placement Test College Math Placement Test Number Theory 1 — Questions and Answers
Question 1: Which of the following numbers is prime?
- 51
- 57
- 61 (Correct answer)
- 91
Correct answer: 61
61 is prime because it has no divisors other than 1 and itself.
Question 2: What is the greatest common divisor (GCD) of 48 and 36?
- 6
- 12 (Correct answer)
- 18
- 24
Correct answer: 12
The GCD of 48 and 36 is 12 since it is the largest number that divides both evenly.
Question 3: What is the least common multiple (LCM) of 8 and 12?
- 16
- 24 (Correct answer)
- 32
- 96
Correct answer: 24
8 = 2³ and 12 = 2²×3, so LCM = 2³×3 = 24.
Question 4: How many prime factors does 360 have counting multiplicity?
- 3
- 4
- 5
- 6 (Correct answer)
Correct answer: 6
360 = 2³×3²×5 gives 3+2+1 = 6 prime factors counting multiplicity.
Question 5: Which of the following is divisible by both 4 and 9?
- 72 (Correct answer)
- 54
- 48
- 81
Correct answer: 72
72 = 4×18 = 9×8, so it is divisible by both 4 and 9.
Question 6: If a number leaves a remainder of 3 when divided by 7, what is the remainder when twice that number is divided by 7?
- 1
- 3
- 6 (Correct answer)
- 2
Correct answer: 6
If n ≡ 3 (mod 7), then 2n ≡ 6 (mod 7), so the remainder is 6.
College Math Placement Test College Math Placement Test Number Theory 1
Which of the following numbers is prime?