The prime factorisation of 3825 is:

Options

A. `3xx5^(2) xx21`
B. `3^(2) xx5^(2) xx35`
C. `3^(2) xx 5^(2) xx17`
D. `3^(2) xx25xx17`

Answer

To find the prime factorization of 3825, we will follow these steps:

### Step 1: Divide by the smallest prime number
Start with the number 3825 and divide it by the smallest prime number, which is 3.

3825 ÷ 3 = 1275

**Hint:** Always start with the smallest prime number when factorizing.

### Step 2: Continue dividing by 3
Now, we will check if 1275 can be divided by 3 again.

1275 ÷ 3 = 425

**Hint:** If a number is divisible by 3, you can keep dividing it by 3 until it is no longer divisible.

### Step 3: Divide by the next smallest prime number
Now, we will check 425 for divisibility by the next smallest prime number, which is 5.

425 ÷ 5 = 85

**Hint:** If a number ends in 0 or 5, it is divisible by 5.

### Step 4: Continue dividing by 5
Next, we will check 85 for divisibility by 5 again.

85 ÷ 5 = 17

**Hint:** Keep dividing by the same prime number as long as the result is still divisible by that prime.

### Step 5: Identify the last prime number
Now we have 17, which is a prime number itself and cannot be divided further.

**Hint:** Remember that prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.

### Step 6: Write the prime factorization
Now we can write the prime factorization of 3825 as:

3825 = 3 × 3 × 5 × 5 × 17

This can also be expressed in exponent form:

3825 = 3² × 5² × 17

### Final Answer
The prime factorization of 3825 is:

**3825 = 3² × 5² × 17**

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