Understanding Prime Factorization
Prime factorization is the process of breaking down a composite number into its prime factors. A prime factor is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
Step-by-Step Prime Factorization of 8788
1. Divide by the Smallest Prime (2)
Since 8788 is even, we start with 2:
- 8788 ÷ 2 = 4394
2. Continue Dividing by 2
Repeat the process:
- 4394 ÷ 2 = 2197 (Now, 2197 is odd, so we move to the next prime.)
3. Check for Divisibility by Next Primes
- 2197 is not divisible by 2, 3, or 5.
- Check 7: 2197 ÷ 7 = 313.857 (not divisible)
- Check 11: 2197 ÷ 11 = 199.727 (not divisible)
- Check 13: 2197 ÷ 13 = 169.0 (divisible)
4. Continue with 13
- 2197 ÷ 13 = 169
5. Factor 169
- 169 = 13 x 13 (or 13^2)
Final Prime Factorization
Collecting all the factors, we have:
- 8788 = 2^2 x 13^3
Conclusion
The complete prime factorization of 8788 is:
- 2^2 x 13^3
This means that 8788 can be expressed as the product of the primes 2 and 13 raised to their respective powers. Understanding this factorization is essential for various mathematical applications, including simplification and finding the greatest common divisor.