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]
