College Math Placement Test College Math Placement Test Number Theory

Question 1

Which of the following numbers is prime?

Accepted Answer

61

Answer

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?

Accepted Answer

12

Answer

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?

Accepted Answer

24

Answer

8 = 2³ and 12 = 2²×3, so LCM = 2³×3 = 24.

Question 4

How many prime factors does 360 have counting multiplicity?

Accepted Answer

6

Answer

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?

Accepted Answer

72

Answer

72 = 4×18 = 9×8, so it is divisible by both 4 and 9.

College Math Placement Test Practice Test