Factors and Multiples — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. What is the GCF of 32 and 48?
A) 4
B) 8
C) 16
D) 32
16 is the largest number that divides both 32 and 48 evenly: 32 ÷ 16 = 2 and 48 ÷ 16 = 3.
2. Which number has exactly 6 factors?
A) 18
B) 20
C) 24
D) 12
The factors of 12 are 1, 2, 3, 4, 6, and 12 -- exactly 6 factors. No other answer choice has exactly 6.
3. What is the LCM of 9 and 15?
A) 30
B) 45
C) 90
D) 135
Multiples of 15 are 15, 30, 45... and multiples of 9 are 9, 18, 27, 36, 45... The smallest they share is 45.
4. Which number is divisible by both 4 and 6 but NOT by 8?
A) 24
B) 36
C) 12
D) 48
12 ÷ 4 = 3 and 12 ÷ 6 = 2, both with no remainder. But 12 ÷ 8 = 1.5, so 12 is not divisible by 8.
Part B: Fill in the Blank
Write the correct answer on each line.
1. The prime factorization of 72 is 2 × 2 × 2 × 3 × 3.
72 = 8 × 9 = (2 × 2 × 2) × (3 × 3). So 72 = 2 × 2 × 2 × 3 × 3, and the missing factor is 3.
2. The GCF of 40 and 60 is 20.
20 is the largest number that divides both 40 and 60 evenly: 40 ÷ 20 = 2 and 60 ÷ 20 = 3.
3. The only even prime number is 2.
2 is prime because its only factors are 1 and 2. Every other even number is divisible by 2, giving it more than two factors.
4. The LCM of 4 and 14 is 28.
Multiples of 14 are 14, 28... and multiples of 4 are 4, 8, 12, 16, 20, 24, 28... The smallest they share is 28.
5. The number 90 has 12 factors in all.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 -- count them and you get 12 total.