Find the prime factorisation of the following numbers:
9261

Options

A. `3 times 3 times 3 times 7 times 7 times 7`
B. `3 times 3 times 3 times 7 times 7 times 5`
C. `2 times 3 times 3 times 7 times 7 times 7`
D. None of these

Answer

To find the prime factorization of the number 9261, we will follow these steps:

### Step 1: Check for divisibility by 3
Since 9261 is an odd number, it cannot be divisible by 2. We will check if it is divisible by 3.

To check for divisibility by 3, we add the digits of the number:
- 9 + 2 + 6 + 1 = 18

Since 18 is divisible by 3, we can conclude that 9261 is also divisible by 3.

### Step 2: Divide by 3
Now we will divide 9261 by 3:
- 9261 ÷ 3 = 3087

### Step 3: Check divisibility of 3087 by 3
Next, we check if 3087 is divisible by 3:
- 3 + 0 + 8 + 7 = 18

Again, since 18 is divisible by 3, we divide 3087 by 3:
- 3087 ÷ 3 = 1029

### Step 4: Check divisibility of 1029 by 3
Now we check if 1029 is divisible by 3:
- 1 + 0 + 2 + 9 = 12

Since 12 is divisible by 3, we divide 1029 by 3:
- 1029 ÷ 3 = 343

### Step 5: Check divisibility of 343
Next, we check if 343 is divisible by 3:
- 3 + 4 + 3 = 10

Since 10 is not divisible by 3, we will check for the next prime number, which is 7.

### Step 6: Divide by 7
Now we check if 343 is divisible by 7:
- 343 ÷ 7 = 49

### Step 7: Factor 49
Next, we factor 49:
- 49 = 7 × 7

### Step 8: Compile the prime factors
Now we can compile all the prime factors we found:
- 9261 = 3 × 3 × 3 × 7 × 7 × 7

This can also be expressed using exponents:
- 9261 = 3^3 × 7^3

### Final Answer
The prime factorization of 9261 is:
- 3^3 × 7^3

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