Understanding Prime Factorization
Prime factorization involves breaking down a composite number into its prime factors, which are the prime numbers that multiply together to form the original number.
Steps to Factorize 35721
1. Check for Small Prime Factors
- Start with the smallest prime number, which is 2. Since 35721 is odd, it cannot be divided by 2.
2. Test for Divisibility by 3
- Add the digits of 35721: 3 + 5 + 7 + 2 + 1 = 18.
- Since 18 is divisible by 3, proceed to divide:
35721 ÷ 3 = 11907.
3. Continue Factoring 11907
- Check 11907 for divisibility by 3 again: 1 + 1 + 9 + 0 + 7 = 18.
- Dividing gives: 11907 ÷ 3 = 3969.
4. Factor 3969
- Similarly, check 3969: 3 + 9 + 6 + 9 = 27.
- Dividing again gives: 3969 ÷ 3 = 1323.
5. Continue with 1323
- Check 1323: 1 + 3 + 2 + 3 = 9.
- Dividing gives: 1323 ÷ 3 = 441.
6. Factor 441
- Check 441: 4 + 4 + 1 = 9.
- Dividing gives: 441 ÷ 3 = 147.
7. Factor 147
- Check 147: 1 + 4 + 7 = 12.
- Dividing gives: 147 ÷ 3 = 49.
8. Factor 49
- 49 is 7 × 7, which are both prime factors.
Final Prime Factorization
- The complete prime factorization of 35721 is:
3 × 3 × 3 × 3 × 7 × 7, or 3^4 × 7^2.