To factorize the number 847293, we'll find its prime factors. Let's go through the factorization process:

1. Check divisibility by the smallest prime number, 2:
   - 847293 is odd, so it is not divisible by 2.

2. Check divisibility by 3:
   - Sum of digits of 847293 = 8 + 4 + 7 + 2 + 9 + 3 = 33, which is divisible by 3.
   - Divide 847293 by 3:  
     \[
     847293 ÷ 3 = 282431
     \]

3. Now, factorize 282431:
   - 282431 is odd, so not divisible by 2.
   - Sum of digits = 2 + 8 + 2 + 4 + 3 + 1 = 20, not divisible by 3.
   - It does not end in 0 or 5, so not divisible by 5.
   - Let's check divisibility by 7:
     \[
     282431 ÷ 7 ≈ 40347.29 \quad \text{(not divisible by 7)}
     \]
   - Continue checking with other primes until we find:
   - 282431 is divisible by 11.
   - Divide by 11:  
     \[
     282431 ÷ 11 = 25675
     \]

4. Now, factorize 25675:
   - 25675 ends in 5, so divisible by 5.
   - Divide by 5:
     \[
     25675 ÷ 5 = 5135
     \]
   - 5135 also ends in 5, so divide by 5 again:
     \[
     5135 ÷ 5 = 1027
     \]
   - Factorize 1027:
     - 1027 is not divisible by 2, 3, 5, or 7.
     - Checking with 13:
       \[
       1027 ÷ 13 = 79 \quad \text{(79 is prime)}
       \]

So, the prime factorization of 847293 is:
\[
847293 = 3 \times 11 \times 5^2 \times 13 \times 79
\]

Would you like a detailed explanation on any step, or do you have any questions?

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Here are five related questions:

1. How can you verify the prime factorization of a number?
2. What is the significance of prime factorization in number theory?
3. How do you determine if a large number is prime?
4. Can every positive integer be expressed as a product of prime numbers?
5. How is prime factorization used in cryptography?

**Tip:** When checking divisibility by primes, start with smaller primes and use divisibility rules to make the process faster.

Discover how to factorize the number 847293 into its prime components with a detailed, step-by-step guide. This problem involves number theory concepts such as divisibility rules and is suitable for students in Grades 9-12.

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