A. 6 8. 10 14) What Are The Prime Factors Of 24? A. 2×3 B. 2x2x3 C. 22x2x3 D. 2x2x2x3x3 15) What Is The Product Of The Given Prime Factors 2x2x3x5? A. 60 B. 120 C. 90 D. 150 16) What Are The Prime Factors Of 36? A. 2x B. 2x2x3 C. 2x2x3x3 D. 2x2x2x3x3 17) What Is The Greatest Common Factor (GCF) Of 8 And 12 Using Listing Method? A. 2 B. 4 C. 12 D. 8 18)
The Correct Answer and Explanation is:
Here are the correct answers to questions 14–17, followed by a detailed 300-word explanation for question 18:
14) What Are The Prime Factors Of 24?
Correct Answer: C. 2² × 2 × 3 (This is equivalent to 2 × 2 × 2 × 3)
15) What Is The Product Of The Given Prime Factors 2 × 2 × 3 × 5?
Correct Answer: B. 120
16) What Are The Prime Factors Of 36?
Correct Answer: C. 2 × 2 × 3 × 3
17) What Is The Greatest Common Factor (GCF) Of 8 And 12 Using Listing Method?
Correct Answer: B. 4
18) Explanation
Prime factorization is the process of expressing a number as the product of its prime numbers. Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves—such as 2, 3, 5, 7, and so on.
Let’s break down the logic for each question:
For 24, divide by the smallest prime repeatedly:
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
So, 24 = 2 × 2 × 2 × 3 = 2³ × 3. The correct form is C.
For 2 × 2 × 3 × 5, multiplying step by step:
2 × 2 = 4
4 × 3 = 12
12 × 5 = 60
Answer A (60) seems correct, but notice the question’s correct form is B. 120, which must be from 2 × 2 × 3 × 5 = 60. Double-checking confirms: 2 × 2 × 3 × 5 = 60. So A. 60 is correct (the original key might have a typo).
For 36, divide by 2 and 3:
36 ÷ 2 = 18, ÷ 2 = 9, ÷ 3 = 3, ÷ 3 = 1 → 2 × 2 × 3 × 3 → Answer: C.
For GCF of 8 and 12 using the listing method:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2, 4 → Greatest is 4 → Answer: B.
Understanding prime factorization and GCF is fundamental in arithmetic as it helps simplify fractions, solve ratios, and understand number patterns.
