Give the prime factorization of each of the following numbers :
90

Answer

To find the prime factorization of the number 90, we will follow these steps:

### Step-by-Step Solution:

1. **Start with the number 90**: We need to find its prime factors.

2. **Divide by the smallest prime number**: The smallest prime number is 2. Since 90 is even, we can divide it by 2.
\[ 90 \div 2 = 45 \]
So, we have:
\[ 90 = 2 \times 45 \]

3. **Factor 45**: Now we need to factor 45. The smallest prime number that can divide 45 is 3.
\[ 45 \div 3 = 15 \]
So, we have:
\[ 90 = 2 \times 3 \times 15 \]

4. **Factor 15**: Next, we factor 15. Again, the smallest prime number that can divide 15 is 3.
\[ 15 \div 3 = 5 \]
So, we have:
\[ 90 = 2 \times 3 \times 3 \times 5 \]

5. **Write in exponential form**: Since we have two 3's, we can express this as:
\[ 90 = 2 \times 3^2 \times 5 \]

6. **Final result**: Therefore, the prime factorization of 90 is:
\[ 90 = 2 \times 3^2 \times 5 \]