Give the prime factorization of each of the following numbers :
` 4335`

Options

A. `3 xx 5 xx 17^(2)`
B. `3 xx 7 xx 17^(2)`
C. `3 xx 9 xx 17^(2)`
D. None of these

Answer

To find the prime factorization of the number 4335, we will follow these steps:

### Step 1: Divide by the smallest prime number
We start by dividing 4335 by the smallest prime number, which is 3.

4335 ÷ 3 = 1445

### Step 2: Continue dividing by prime numbers
Next, we check if 1445 can be divided by 3 again. Since the sum of the digits (1 + 4 + 4 + 5 = 14) is not divisible by 3, we move to the next prime number, which is 5.

1445 ÷ 5 = 289

### Step 3: Factor the next number
Now we need to factor 289. We check if it can be divided by 5 or 7. It cannot, but it can be divided by 17.

289 ÷ 17 = 17

### Step 4: Write down the factors
Now we can write down all the prime factors we have found:

- From Step 1: 3
- From Step 2: 5
- From Step 3: 17 (and since 17 was divided again, we write it twice)

### Final Result
Thus, the prime factorization of 4335 is:

**3 × 5 × 17 × 17** or **3 × 5 × 17²**

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