1.3 Show through factorizing that 899 is not a prime numb

Question

UpStudy AI · Accepted Answer

1. **Understanding the Problem**

We need to show that $$899$$ is not a prime number by factorizing it into two or more factors greater than $$1$$.

2. **Checking Divisibility**

A prime number has no divisors other than $$1$$ and itself. To test if $$899$$ can be factorized, we first check divisibility by small prime numbers. Note that the square root of $$899$$ is approximately
   $$
   \sqrt{899} \approx 30.
   $$
   Therefore, it is sufficient to check for factors less than or equal to $$30$$.

3. **Testing Potential Factors**

We test divisibility by some of the small primes:
   
   - $$899 \div 2$$ is not an integer (since $$899$$ is odd).
   - $$899 \div 3$$: The sum of the digits is $$8 + 9 + 9 = 26$$, which is not divisible by $$3$$.
   - $$899 \div 5$$ is not an integer (since $$899$$ does not end in $$0$$ or $$5$$).
   - Continue testing with primes like $$7, 11, 13, 17, 19,$$ and $$23$$ until a divisor is found.
   
4. **Finding the Correct Factors**

When testing $$29$$:
   $$
   899 \div 29 = 31
   $$
   Since $$31$$ is an integer and also a prime number, we have found a successful factorization.

5. **Conclusion**

We have factorized $$899$$ as:
   $$
   899 = 29 \times 31.
   $$
   Since both $$29$$ and $$31$$ are prime numbers, $$899$$ is not a prime number.
$$899$$ is not a prime number because it can be factored into $$29 \times 31$$.

1.3 Show through factorizing that 899 is not a prime numb

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Pre Algebra Questions