Factors and Multiples — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. How many factors does 48 have?
A) 8
B) 9
C) 10
D) 12
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 — that is 10 factors.
2. How many prime numbers are between 20 and 30?
A) 1
B) 2
C) 3
D) 4
The prime numbers between 20 and 30 are 23 and 29 — that is 2 primes.
3. What is the least common multiple of 8 and 12?
A) 16
B) 24
C) 48
D) 96
Multiples of 12: 12, 24... Multiples of 8: 8, 16, 24... LCM = 24.
4. Is 51 prime or composite?
A) Prime
B) Composite
C) Neither
D) Both
51 = 3 × 17, so it has factors other than 1 and itself. It is composite.
Part B: Fill in the Blank
Write the correct answer on each line.
1. The GCF of 24 and 36 is 12.
Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. Greatest common factor = 12.
2. All prime numbers greater than 2 are odd numbers.
Any even number greater than 2 is divisible by 2, so it cannot be prime. All primes greater than 2 must be odd.
3. The number 100 has 5 factor pairs.
Factor pairs of 100: (1,100), (2,50), (4,25), (5,20), (10,10) — 5 pairs.
4. The LCM of 5 and 12 is 60.
5 and 12 share no common factors, so LCM = 5 × 12 = 60.
5. The prime factorization of 36 is 2 × 2 × 3 × 3.
36 = 2² × 3² = 2 × 2 × 3 × 3.