Find the prime factorisation of:
756

Answer

To find the prime factorization of 756, we will divide the number by the smallest prime numbers until we reach 1. Here are the steps:

### Step 1: Divide by 2
Since 756 is an even number, we can start by dividing it by 2.

\[ 756 \div 2 = 378 \]

### Step 2: Divide by 2 again
Now we take 378, which is also even, and divide it by 2 again.

\[ 378 \div 2 = 189 \]

### Step 3: Divide by 3
Next, we take 189. Since 189 is not even, we check the next smallest prime number, which is 3.

\[ 189 \div 3 = 63 \]

### Step 4: Divide by 3 again
Now we take 63 and divide it by 3.

\[ 63 \div 3 = 21 \]

### Step 5: Divide by 3 again
Next, we take 21 and divide it by 3 once more.

\[ 21 \div 3 = 7 \]

### Step 6: Divide by 7
Finally, we take 7, which is a prime number, and divide it by itself.

\[ 7 \div 7 = 1 \]

### Conclusion
Now we can write the prime factorization of 756 as:

\[ 756 = 2 \times 2 \times 3 \times 3 \times 3 \times 7 \]

This can also be expressed in exponential form as:

\[ 756 = 2^2 \times 3^3 \times 7^1 \]