Find the prime factorisation of
`230`

Options

A. `2 xx 5 xx 23`
B. `2 xx 3 xx 23`
C. `2 xx 5 xx 13`
D. `2 xx 5 xx 19`

Answer

To find the prime factorization of the number 230, we will follow these steps:

### Step 1: Start with the smallest prime number
The smallest prime number is 2. We will check if 230 is divisible by 2.

**Calculation:**
230 ÷ 2 = 115

Since 230 is divisible by 2, we can write:
\[ 230 = 2 \times 115 \]

### Step 2: Factor the next number (115)
Now we need to factor 115. We will check if it is divisible by the next smallest prime number, which is 3.

**Calculation:**
115 ÷ 3 = 38.33 (not divisible)

Since 115 is not divisible by 3, we will check the next prime number, which is 5.

**Calculation:**
115 ÷ 5 = 23

Since 115 is divisible by 5, we can write:
\[ 115 = 5 \times 23 \]

### Step 3: Check if 23 is a prime number
Now we need to check if 23 is a prime number. A prime number is only divisible by 1 and itself.

Since 23 cannot be divided by any prime number less than or equal to its square root (which is approximately 4.79), we check 2, 3 (both do not divide 23). Thus, 23 is a prime number.

### Step 4: Combine all factors
Now we can combine all the factors we found:
\[ 230 = 2 \times 5 \times 23 \]

### Final Result
Thus, the prime factorization of 230 is:
\[ 2 \times 5 \times 23 \]

---