College Math Placement Test College Math Placement Test Number Theory 2

Question 1

What is the prime factorization of 180?

Accepted Answer

2² × 3² × 5

Answer

180 = 4×45 = 4×9×5 = 2²×3²×5.

Question 2

Which pair of numbers is relatively prime (coprime)?

Accepted Answer

14 and 27

Answer

14 = 2×7 and 27 = 3³ share no common factors, so GCD(14, 27) = 1.

Question 3

A number is divisible by 6 if and only if it is:

Accepted Answer

Divisible by both 2 and 3

Answer

Since 6 = 2×3 and GCD(2,3) = 1, divisibility by 6 requires divisibility by both 2 and 3.

Question 4

What is the LCM of 6, 10, and 15?

Accepted Answer

30

Answer

6=2×3, 10=2×5, 15=3×5, so LCM = 2×3×5 = 30.

Question 5

How many positive divisors does 100 have?

Accepted Answer

9

Answer

100 = 2²×5², so the number of divisors = (2+1)(2+1) = 9.

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