Give the prime factorization of each of the following numbers :
8712

Answer

To find the prime factorization of the number 8712, we will follow these steps:

### Step 1: Divide by the smallest prime number
Start by dividing 8712 by the smallest prime number, which is 2, since 8712 is an even number.

\[ 8712 \div 2 = 4356 \]

### Step 2: Continue dividing by 2
Since 4356 is also even, we can divide it by 2 again.

\[ 4356 \div 2 = 2178 \]

### Step 3: Divide by 2 again
Continue dividing by 2.

\[ 2178 \div 2 = 1089 \]

### Step 4: Check if 1089 is divisible by 2
1089 is not even, so we cannot divide it by 2 anymore. Next, we will try the next smallest prime number, which is 3.

### Step 5: Divide by 3
Check if 1089 is divisible by 3. The sum of the digits (1 + 0 + 8 + 9 = 18) is divisible by 3.

\[ 1089 \div 3 = 363 \]

### Step 6: Divide by 3 again
Now, divide 363 by 3.

\[ 363 \div 3 = 121 \]

### Step 7: Check if 121 is a prime number
121 is not divisible by 2 or 3, so we try the next prime number, which is 11.

### Step 8: Divide by 11
Check if 121 is divisible by 11.

\[ 121 \div 11 = 11 \]

### Step 9: Divide by 11 again
Finally, divide 11 by 11.

\[ 11 \div 11 = 1 \]

### Conclusion
Now we can write the prime factorization of 8712:

\[ 8712 = 2^3 \times 3^2 \times 11^2 \]

### Summary of Prime Factorization
The prime factorization of 8712 is:

\[ 8712 = 2 \times 2 \times 2 \times 3 \times 3 \times 11 \times 11 \]