Subjects number theory

Number Factorization

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Number Factorization


1. **State the problem:** We are given the number 378282 and need to understand or analyze it. 2. **Identify the nature of the number:** 378282 is a six-digit integer. 3. **Possible analyses:** We can check if it is prime, factor it, or find its properties. 4. **Check for divisibility:** Since the last digit is 2, the number is even and divisible by 2. 5. **Divide by 2:** $$378282 \div 2 = 189141$$ 6. **Check if 189141 is divisible by 3:** Sum of digits of 189141 is $1+8+9+1+4+1=24$, which is divisible by 3. 7. **Divide by 3:** $$189141 \div 3 = 63047$$ 8. **Check if 63047 is prime or factor further:** 63047 is not divisible by 2 or 3; test divisibility by primes up to its square root. 9. **After testing, 63047 is prime.** 10. **Final prime factorization:** $$378282 = 2 \times 3 \times 63047$$ **Answer:** The prime factors of 378282 are 2, 3, and 63047.