AMC 8 Number Theory & Divisibility

Question 1

What is the greatest common factor (GCF) of 48 and 36?

Accepted Answer

12

Answer

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?

Accepted Answer

61

Answer

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?

Accepted Answer

24

Answer

The LCM of 6 and 8 is 24, the smallest positive number divisible by both.

Question 4

How many positive factors does 36 have?

Accepted Answer

9

Answer

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?

Accepted Answer

28

Answer

The factors of 12 are 1, 2, 3, 4, 6, 12, and 1+2+3+4+6+12 = 28.

AMC 8 - American Mathematics Competition 8 Practice Test