Factors and Multiples — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Hot dogs come in packs of 8 and buns in packs of 6. What is the fewest of each you need so they match?
A) 16
B) 24
C) 32
D) 48
LCM(8, 6) = 24. You need 3 packs of hot dogs (3×8=24) and 4 packs of buns (4×6=24).
2. A teacher wants to arrange 60 chairs in equal rows. How many ways can she do it?
A) 8
B) 10
C) 12
D) 14
60 has 12 factors: 1,2,3,4,5,6,10,12,15,20,30,60 — each represents a valid row arrangement.
3. Which number is NOT divisible by 9?
A) 72
B) 54
C) 35
D) 81
Digit sum of 35 = 3+5 = 8, which is not divisible by 9. Therefore 35 is not divisible by 9.
4. Sam has 18 red marbles and 24 blue marbles. He puts them in groups with equal reds and equal blues. What is the greatest number of groups?
A) 3
B) 4
C) 6
D) 9
GCF(18, 24) = 6. Sam can make 6 groups with 3 red and 4 blue marbles each.
Part B: Fill in the Blank
Write the correct answer on each line.
1. Buses leave every 15 minutes and trains leave every 20 minutes. They both leave at 8:00 AM and next leave together at 8:60 AM.
LCM(15, 20) = 60. Both leave together again 60 minutes after 12:00 (at 1:00 PM).
2. The GCF of 30 and 45 is 15.
Factors of 30: 1,2,3,5,6,10,15,30. Factors of 45: 1,3,5,9,15,45. GCF = 15.
3. A number is divisible by 6 if it is divisible by both 2 and 3.
6 = 2 × 3. A number divisible by both 2 and 3 must be divisible by 6.
4. The LCM of 9 and 12 is 36.
Multiples of 12: 12, 24, 36... Multiples of 9: 9, 18, 27, 36... LCM = 36.
5. There are 8 prime numbers less than 20.
Primes less than 20: 2, 3, 5, 7, 11, 13, 17, 19 — that is 8 prime numbers.