AMC 8 Number Theory & Divisibility 3

Question 1

What is the prime factorization of 120?

Accepted Answer

2³ × 3 × 5

Answer

2² × 3 × 5

Answer

2³ × 3² × 5

Answer

2 × 3 × 5²

Question 2

How many perfect squares are there from 1 to 200, inclusive?

Accepted Answer

14

Answer

12

Answer

13

Answer

15

Question 3

What is the GCF of 2³ × 3² and 2² × 3⁴?

Accepted Answer

36

Answer

12

Answer

72

Answer

18

Question 4

What is the smallest positive integer n such that n² is divisible by 12?

Accepted Answer

6

Answer

2

Answer

4

Answer

12

Question 5

How many three-digit numbers have digits that are strictly increasing from left to right (each digit greater than the one before)?

Accepted Answer

84

Answer

56

Answer

120

Answer

210

Question 6

What is the remainder when 2²⁵ is divided by 3?

Accepted Answer

2

Answer

0

Answer

1

Answer

3