Question
Write the following as a ploduct of its prome factors \( \begin{array}{lll}\text { a) } 18 & \text { (d) } 150 & \text { (c) } 20 \\ \text { (d) } 120 & \text { (a) } 154 & \text { (f) } 325\end{array} \) \( \begin{array}{lll}\text { (g) } 78 & \text { (h) } 164 & \end{array} \)
Ask by Donnelly Hobbs. in South Africa
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the numbers expressed as the product of their prime factors:
1. 18 = 2 × 3 × 3 = 2 × 3²
2. 150 = 2 × 3 × 5 × 5 = 2 × 3 × 5²
3. 20 = 2 × 2 × 5 = 2² × 5
4. 120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5
5. 154 = 2 × 7 × 11
6. 325 = 5 × 5 × 13 = 5² × 13
7. 78 = 2 × 3 × 13
8. 164 = 2 × 2 × 41 = 2² × 41
Solution
Below are the numbers written as the product of their prime factors:
1. 18 = 2 × 3 × 3 = 2 × 3²
2. 150 = 2 × 75 = 2 × 3 × 25 = 2 × 3 × 5 × 5 = 2 × 3 × 5²
3. 20 = 2 × 10 = 2 × 2 × 5 = 2² × 5
4. 120 = 2 × 60 = 2 × 2 × 30 = 2 × 2 × 2 × 15 = 2³ × 15 = 2³ × 3 × 5
5. 154 = 2 × 77 = 2 × 7 × 11
6. 325 = 5 × 65 = 5 × 5 × 13 = 5² × 13
7. 78 = 2 × 39 = 2 × 3 × 13
8. 164 = 2 × 82 = 2 × 2 × 41 = 2² × 41
Each number has been broken down to its prime factors.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
Sure! Here are the prime factorization for each of the given numbers: a) \( 18 = 2 \times 3^2 \) b) \( 150 = 2 \times 3 \times 5^2 \) c) \( 20 = 2^2 \times 5 \) d) \( 120 = 2^3 \times 3 \times 5 \) e) \( 154 = 2 \times 7 \times 11 \) f) \( 325 = 5^2 \times 13 \) g) \( 78 = 2 \times 3 \times 13 \) h) \( 164 = 2^2 \times 41 \)
