Factors and Multiples — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The GCF of 16 and 24 is 8.
The factors of 16 are 1, 2, 4, 8, 16 and the factors of 24 include 1, 2, 4, 8. The largest shared factor is 8.
2. The LCM of 6 and 10 is 30.
Multiples of 10 are 10, 20, 30... and multiples of 6 are 6, 12, 18, 24, 30... The first one they share is 30.
3. The prime factorization of 24 is 2 × 2 × 2 × 3.
24 = 2 × 12, then 12 = 2 × 6, then 6 = 2 × 3. So 24 = 2 × 2 × 2 × 3, and the missing factor is 3.
4. The GCF of two prime numbers is always 1.
Each prime number only has factors 1 and itself, so two different primes share no factor other than 1.
5. The prime factorization of 50 is 2 × 5 × 5.
50 = 2 × 25, and 25 = 5 × 5. So the full prime factorization is 2 × 5 × 5, and the missing factor is 5.
6. The LCM of 7 and 14 is 14.
Since 14 is already a multiple of 7 (7 × 2 = 14), the LCM is simply 14.
7. The GCF of 36 and 48 is 12.
The largest number that divides both 36 and 48 evenly is 12, since 36 ÷ 12 = 3 and 48 ÷ 12 = 4.
8. The prime factorization of 60 is 2 × 2 × 3 × 5.
60 = 2 × 30, 30 = 2 × 15, 15 = 3 × 5. So 60 = 2 × 2 × 3 × 5, and the missing factor is 5.
9. The LCM of 8 and 10 is 40.
Multiples of 10 are 10, 20, 30, 40... and multiples of 8 are 8, 16, 24, 32, 40... The first they share is 40.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each number to its correct classification.
29
→ Prime number
Composite, divisible by 5
45
→ Composite, divisible by 5
Neither prime nor composite
64
→ Composite, perfect square
Prime number
1
→ Neither prime nor composite
Composite, perfect square
Correct matches: 29 → Prime number; 45 → Composite, divisible by 5; 64 → Composite, perfect square; 1 → Neither prime nor composite.