Pregunta
\( \left.\begin{array}{l}\text { 1. Which of these numbers are prime numbers? } \\ \text { 2. List the factors of these numbers: } \\ \begin{array}{lllll}\text { a) } 15 & \text { b) } 24 & \text { c) } 36 & \text { d) } 105 & \text { e) } 300\end{array} \\ \begin{array}{lllll}\text { 3. List the first five multiples of these numbers: } \\ \begin{array}{llll}\text { a) } 6 & \text { b) } 9 & \text { c) } 12 & \text { d) } 20\end{array} & \text { e) } 100\end{array} \\ \text { 4. List all the multiples of } 4 \text { that are between } 10 \text { and } 30\end{array}\right] \).
Ask by Spencer Bryant. in South Africa
Jan 30,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
**1. Prime Numbers:**
- 15: Not prime
- 24: Not prime
- 36: Not prime
- 105: Not prime
- 300: Not prime
**2. Factors:**
- **15:** 1, 3, 5, 15
- **24:** 1, 2, 3, 4, 6, 8, 12, 24
- **36:** 1, 2, 3, 4, 6, 9, 12, 18, 36
- **105:** 1, 3, 5, 7, 15, 21, 35, 105
- **300:** 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
**3. First Five Multiples:**
- **6:** 6, 12, 18, 24, 30
- **9:** 9, 18, 27, 36, 45
- **12:** 12, 24, 36, 48, 60
- **20:** 20, 40, 60, 80, 100
- **100:** 100, 200, 300, 400, 500
**4. Multiples of 4 Between 10 and 30:**
- 12, 16, 20, 24, 28
Solución
Sure, I'd be happy to help you with these math problems!
---
### **1. Which of these numbers are prime numbers?**
*It seems like the specific numbers to evaluate for primality aren't provided. Could you please provide the list of numbers you'd like to check?*
---
### **2. List the factors of these numbers:**
**a) 15**
Factors of 15 are the numbers that divide 15 without leaving a remainder.
- **1**, **3**, **5**, **15**
**b) 24**
Factors of 24:
- **1**, **2**, **3**, **4**, **6**, **8**, **12**, **24**
**c) 36**
Factors of 36:
- **1**, **2**, **3**, **4**, **6**, **9**, **12**, **18**, **36**
**d) 105**
Factors of 105:
- **1**, **3**, **5**, **7**, **15**, **21**, **35**, **105**
**e) 300**
Factors of 300:
- **1**, **2**, **3**, **4**, **5**, **6**, **10**, **12**, **15**, **20**, **25**, **30**, **50**, **60**, **75**, **100**, **150**, **300**
---
### **3. List the first five multiples of these numbers:**
**a) 6**
Multiples of 6:
1. **6**
2. **12**
3. **18**
4. **24**
5. **30**
**b) 9**
Multiples of 9:
1. **9**
2. **18**
3. **27**
4. **36**
5. **45**
**c) 12**
Multiples of 12:
1. **12**
2. **24**
3. **36**
4. **48**
5. **60**
**d) 20**
Multiples of 20:
1. **20**
2. **40**
3. **60**
4. **80**
5. **100**
**e) 100**
Multiples of 100:
1. **100**
2. **200**
3. **300**
4. **400**
5. **500**
---
### **4. List all the multiples of 4 that are between 10 and 30**
To find the multiples of 4 between 10 and 30, divide the range by 4 and list the integers:
- **12** (4 × 3)
- **16** (4 × 4)
- **20** (4 × 5)
- **24** (4 × 6)
- **28** (4 × 7)
**Multiples of 4 between 10 and 30:**
- **12**, **16**, **20**, **24**, **28**
---
If you provide the specific numbers for question 1, I'd be glad to help identify which of them are prime!
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Simplifique esta solución Beyond the Answer
Many people think of prime numbers as just a mystery of math, but they have been studied for centuries! The ancient Greeks were fascinated by primes, with Euclid proving that there are infinitely many primes. This laid the groundwork for modern number theory. Fun fact: the largest known prime number has over 24 million digits! Understanding factors and multiples is essential not just in math class, but in real life too! Whether you’re splitting a pizza (factors) or planning your next party (multiples), this knowledge is super practical. If you're trying to avoid common mistakes, remember that prime numbers only have two factors: 1 and themselves—so skip over numbers like 15 and 24 when searching for them!
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