Express as power of prime factors A ]4193     B] 125

To express the numbers as products of their prime factors, we will break down each number into its prime components.

### A) \(4193\)

Let's check if \(4193\) can be factored into prime numbers. We'll start by testing divisibility by smaller prime numbers (like \(2, 3, 5, 7, \) etc.) until we find any factor or confirm that it's prime.

After testing divisibility up to \(\sqrt{4193} \approx 64.74\), we find that:

- **4193** is not divisible by any of these smaller primes.
- Therefore, **4193** is a prime number itself.

So, the prime factorization of **4193** is:
\[
4193 = 4193^1
\]

### B) \(125\)

Next, we factor **125** into its prime components.

- **125** is divisible by \(5\):
\[
125 \div 5 = 25
\]
- **25** is also divisible by \(5\):
\[
25 \div 5 = 5
\]
- **5** is a prime number.

Thus, the prime factorization of **125** is:
\[
125 = 5 \times 5 \times 5 = 5^3
\]

### Final Results:

- **A)** \(4193 = 4193^1\) (a prime number itself)
- **B)** \(125 = 5^3\)

Would you like more details or have any questions?

### Related Questions:

1. How do you determine if a large number is prime?
2. Why is \(4193\) considered a prime number?
3. How do you factor a composite number into its prime factors efficiently?
4. What is the significance of expressing a number as a product of its prime factors?
5. How do you find the greatest common divisor (GCD) using prime factorization?

**Tip:** To check the primality of a number, you only need to test for divisibility by primes up to its square root.

Express as power of prime factors A] 4193 B] 125

Discover the prime factorization of the numbers 4193 and 125. Learn how to express 4193 as a prime number and break down 125 into its prime factors, using number theory and divisibility rules. Suitable for students in Grades 8-10.

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