The answer is not correct. Let's find the correct Highest Common Factor (HCF) of the numbers 4 and 15 using the prime factorization method in a step-by-step fashion.
### Step-by-Step Solution
1. Prime Factorization:
- For [tex]\( 4 \)[/tex]:
The prime factors of 4 are [tex]\( 2 \times 2 \)[/tex]. So, we can write:
[tex]\[
4 = 2^2
\][/tex]
- For [tex]\( 15 \)[/tex]:
The prime factors of 15 are [tex]\( 3 \times 5 \)[/tex]. So, we can write:
[tex]\[
15 = 3 \times 5
\][/tex]
2. Identify Common Factors:
Now, we compare the prime factors of 4 and 15 to identify any common factors:
- Factors of 4: [tex]\( 2 \)[/tex]
- Factors of 15: [tex]\( 3, 5 \)[/tex]
As we can see, there are no common prime factors between 4 and 15.
3. Conclusion:
When there are no common prime factors between two numbers, those numbers are termed co-prime (or relatively prime). The Highest Common Factor (HCF) of co-prime numbers is always 1 because 1 is the only number that can divide both of them without leaving a remainder.
### Final Answer:
Therefore, the HCF of 4 and 15 is:
[tex]\[
\boxed{1}
\][/tex]
