Simplify by prime factorization:

[tex]\[\frac{45}{12}\][/tex]

Choose the correct option:

1. [tex]$\square$[/tex]
2. [tex]$\square$[/tex]
3. [tex]$\square$[/tex]

a. [tex]$\frac{10}{1}$[/tex]
b. [tex]$\frac{\not Z \times 3 \times 5}{2 \times 2 \times \not 2}$[/tex]
c. [tex]$\frac{15}{4}$[/tex]
d. [tex]$\frac{3 \times 3 \times 5}{2 \times 2 \times 3}$[/tex]

To simplify the fraction [tex]$\frac{45}{12}$[/tex] using prime factorization, follow these steps:

1. Prime Factorization of 45:
- 45 can be divided by 3 (which is a prime number).
- [tex]$45 \div 3 = 15$[/tex]
- 15 can also be divided by 3.
- [tex]$15 \div 3 = 5$[/tex]
- 5 is a prime number.

Thus, the prime factorization of 45 is [tex]$3 \times 3 \times 5$[/tex].

2. Prime Factorization of 12:
- 12 can be divided by 2 (which is a prime number).
- [tex]$12 \div 2 = 6$[/tex]
- 6 can be divided by 2 again.
- [tex]$6 \div 2 = 3$[/tex]
- 3 is a prime number.

Therefore, the prime factorization of 12 is [tex]$2 \times 2 \times 3$[/tex].

3. Cancel Common Factors:
- Both the numerator and the denominator have a common factor of 3. Cancel out one 3 from each.

After cancelling, we have:
- Numerator: [tex]$3 \times 5$[/tex]
- Denominator: [tex]$2 \times 2$[/tex]

4. Multiply Remaining Factors:
- In the numerator: [tex]$3 \times 5 = 15$[/tex]
- In the denominator: [tex]$2 \times 2 = 4$[/tex]

5. Simplified Fraction:
- Thus, the fraction [tex]$\frac{45}{12}$[/tex] simplifies to [tex]$\frac{15}{4}$[/tex].

With the above steps, your fraction is successfully simplified using prime factorization to [tex]$\frac{15}{4}$[/tex].