Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

36. Find all the factors of 24.

37. Which of the numbers [tex]2, 3, 4, 5, 9, \text{ and } 10[/tex] are factors of 240?

38. Write the prime factorization of 50.

Sagot :

GinnyAnswer
Certainly! Let's address each of the questions one by one in a detailed manner.

### 36. Find all the factors of 24

To find the factors of 24, we need to identify all the numbers that divide 24 completely without leaving any remainder.

- Start with 1 (because 1 is a factor of every number): [tex]\( 24 \div 1 = 24 \)[/tex]
- Check 2: [tex]\( 24 \div 2 = 12 \)[/tex]
- Check 3: [tex]\( 24 \div 3 = 8 \)[/tex]
- Check 4: [tex]\( 24 \div 4 = 6 \)[/tex]
- Check 6: [tex]\( 24 \div 6 = 4 \)[/tex]
- Check 8: [tex]\( 24 \div 8 = 3 \)[/tex]
- Check 12: [tex]\( 24 \div 12 = 2 \)[/tex]
- Check 24: [tex]\( 24 \div 24 = 1 \)[/tex]

Thus, all factors of 24 are:
[tex]\[ 1, 2, 3, 4, 6, 8, 12, 24 \][/tex]

### 37. Which of the numbers [tex]\( 2, 3, 4, 5, 9, \text{ and } 10 \)[/tex] are factors of 240?

To determine which of the given numbers are factors of 240, we will check if 240 can be divided exactly by each of these numbers.

- Check 2: [tex]\( 240 \div 2 = 120 \)[/tex] (No remainder)
- Check 3: [tex]\( 240 \div 3 = 80 \)[/tex] (No remainder)
- Check 4: [tex]\( 240 \div 4 = 60 \)[/tex] (No remainder)
- Check 5: [tex]\( 240 \div 5 = 48 \)[/tex] (No remainder)
- Check 9: [tex]\( 240 \div 9 \approx 26.67 \)[/tex] (This is not an integer, so 9 is not a factor)
- Check 10: [tex]\( 240 \div 10 = 24 \)[/tex] (No remainder)

Hence, the numbers [tex]\( 2, 3, 4, 5, \text{ and } 10 \)[/tex] are factors of 240.

### 38. Write the prime factorization of 50

To find the prime factorization, we need to break down 50 into its prime factors:

- Start with the smallest prime number, 2: [tex]\( 50 \div 2 = 25 \)[/tex]. So, 2 is a factor.
- Next, move to the next smallest prime number, 3. [tex]\( 25 \)[/tex] is not divisible by 3.
- Move to the next prime number, 5: [tex]\( 25 \div 5 = 5 \)[/tex]. So, another factor is 5.
- Continue with 5: [tex]\( 5 \div 5 = 1 \)[/tex]. So, include another 5.

Therefore, the prime factorization of 50 is:
[tex]\[ 2, 5, 5 \][/tex]

### Summary

#### 36. Factors of 24:
[tex]\[ 1, 2, 3, 4, 6, 8, 12, 24 \][/tex]

#### 37. Factors of 240 among [tex]\( 2, 3, 4, 5, 9, \text{ and } 10 \)[/tex]:
[tex]\[ 2, 3, 4, 5, 10 \][/tex]

#### 38. Prime factorization of 50:
[tex]\[ 2, 5, 5 \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.