Find the prime factorisation of the following numbers:
2280

Options

A. `2 times 2 times 2 times 3 times 5 times 19`
B. `2 times 2 times 2 times 3 times 5 times 17`
C. `2 times 2 times 2 times 3 times 5 times 15`
D. `2 times 2 times 3 times 3 times 5 times 19`

Answer

To find the prime factorization of the number 2280, we will follow these steps:

### Step 1: Start with the number 2280
We begin with the number 2280.

### Step 2: Divide by the smallest prime number
Since 2280 is an even number, we can divide it by 2, the smallest prime number.

2280 ÷ 2 = 1140

### Step 3: Continue dividing by 2
We can see that 1140 is also even, so we divide by 2 again.

1140 ÷ 2 = 570

### Step 4: Divide by 2 once more
570 is still even, so we divide by 2 again.

570 ÷ 2 = 285

### Step 5: Check for divisibility by the next smallest prime
Now, we check 285. It is not even, so we check the next prime number, which is 3. To check if 285 is divisible by 3, we can sum the digits (2 + 8 + 5 = 15), and since 15 is divisible by 3, we divide by 3.

285 ÷ 3 = 95

### Step 6: Check for divisibility by the next prime
Next, we check 95. The last digit is 5, so it is divisible by 5.

95 ÷ 5 = 19

### Step 7: Identify if the last number is prime
Now we have 19. Since 19 is a prime number, we cannot factor it further.

### Step 8: Write the prime factorization
Now we can write the prime factorization of 2280 as:

2280 = 2 × 2 × 2 × 3 × 5 × 19

Or, we can express it using exponents:

2280 = 2^3 × 3^1 × 5^1 × 19^1

### Final Answer:
The prime factorization of 2280 is:
\[ 2^3 \times 3^1 \times 5^1 \times 19^1 \]

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