Find the prime factorisation of the numbers given below:
90720

Answer

To find the prime factorization of the number 90,720, we will use the prime factor tree method. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Start with the number 90,720.**
- We will divide it by the smallest prime number, which is 2.

2. **Divide 90,720 by 2:**
- \( 90,720 \div 2 = 45,360 \)

3. **Continue dividing by 2:**
- \( 45,360 \div 2 = 22,680 \)
- \( 22,680 \div 2 = 11,340 \)
- \( 11,340 \div 2 = 5,670 \)
- \( 5,670 \div 2 = 2,835 \)

4. **Now, 2,835 is not divisible by 2, so we move to the next prime number, which is 3:**
- \( 2,835 \div 3 = 945 \)
- \( 945 \div 3 = 315 \)
- \( 315 \div 3 = 105 \)
- \( 105 \div 3 = 35 \)

5. **Now, 35 is not divisible by 3, so we move to the next prime number, which is 5:**
- \( 35 \div 5 = 7 \)

6. **Finally, we reach the prime number 7:**
- \( 7 \div 7 = 1 \)

7. **Now we can write down all the prime factors we used:**
- We divided by 2 five times, by 3 four times, and by 5 and 7 once each.

8. **Thus, the prime factorization of 90,720 is:**
- \( 90,720 = 2^5 \times 3^4 \times 5^1 \times 7^1 \)

### Final Answer:
The prime factorization of 90,720 is \( 2^5 \times 3^4 \times 5^1 \times 7^1 \).

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