Write the prime factorization of 158 . Use exponents when appropriate and order the factors from least to greatest (for example, $$ 2^{2} \cdot 3 \cdot 5 $$ ).

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UpStudy AI · Accepted Answer

We start by checking if $$158$$ is divisible by the smallest prime number, $$2$$.

1. **Division by 2:**

Since $$158$$ is even, it is divisible by $$2$$. Dividing $$158$$ by $$2$$, we get:
   
   $$
   158 \div 2 = 79
   $$
   
   This gives us:
   
   $$
   158 = 2 \cdot 79
   $$

2. **Checking if 79 is Prime:**

We now check whether $$79$$ is a prime number. A prime number has no positive divisors other than $$1$$ and itself. Testing divisibility by the primes less than $$\sqrt{79} \approx 8.9$$ (i.e., $$2$$, $$3$$, $$5$$, and $$7$$) shows that none of these divide $$79$$ evenly. Therefore, $$79$$ is indeed a prime number.
   
3. **Final Prime Factorization:**

Since both $$2$$ and $$79$$ are prime and the factors are already ordered from least to greatest, the prime factorization of $$158$$ is:
   
   $$
   2 \cdot 79
   $$

Thus, the prime factorization of $$158$$ is:

$$
\boxed{2 \cdot 79}
$$
The prime factorization of 158 is $$2 \cdot 79$$.

Write the prime factorization of 158 . Use exponents when appropriate and order the factors from least to greatest (for example, \( 2^{2} \cdot 3 \cdot 5 \) ).

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