Write the prime factorisation of 8190.

Answer

To find the prime factorization of 8190, we will follow a systematic approach of dividing the number by prime numbers until we reach 1.

### Step-by-Step Solution:

1. **Start with the number 8190.**
- We will check for divisibility by the smallest prime number, which is 2.

2. **Divide by 2:**
- 8190 is even, so we can divide it by 2.
- \( 8190 \div 2 = 4095 \)
- So, we have: \( 8190 = 2 \times 4095 \)

3. **Next, check 4095 for divisibility by the next smallest prime, which is 3:**
- To check divisibility by 3, we can sum the digits of 4095: \( 4 + 0 + 9 + 5 = 18 \) (which is divisible by 3).
- Now, divide 4095 by 3:
- \( 4095 \div 3 = 1365 \)
- So, we have: \( 8190 = 2 \times 3 \times 1365 \)

4. **Now, check 1365 for divisibility by 3 again:**
- Sum the digits: \( 1 + 3 + 6 + 5 = 15 \) (which is also divisible by 3).
- Divide 1365 by 3:
- \( 1365 \div 3 = 455 \)
- So, we have: \( 8190 = 2 \times 3^2 \times 455 \)

5. **Next, check 455 for divisibility by the next prime, which is 5:**
- 455 ends in 5, so it is divisible by 5.
- Divide 455 by 5:
- \( 455 \div 5 = 91 \)
- So, we have: \( 8190 = 2 \times 3^2 \times 5 \times 91 \)

6. **Now, check 91 for divisibility by the next prime, which is 7:**
- \( 91 \div 7 = 13 \)
- So, we have: \( 8190 = 2 \times 3^2 \times 5 \times 7 \times 13 \)

7. **At this point, we have reached all prime factors.**
- The prime factorization of 8190 is:
- \( 8190 = 2^1 \times 3^2 \times 5^1 \times 7^1 \times 13^1 \)

### Final Answer:
The prime factorization of 8190 is \( 2^1 \times 3^2 \times 5^1 \times 7^1 \times 13^1 \).

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