What is the prime factorization of 46?
Understand the Problem
The question is asking for the prime factorization of the number 46, which involves breaking it down into its prime factors.
Answer
The prime factorization of 46 is $2 \times 23$.
Answer for screen readers
The prime factorization of 46 is $2 \times 23$.
Steps to Solve
- Identify if 46 is an even number
Since 46 ends in a 6, it is an even number. Therefore, it is divisible by 2, the smallest prime number.
- Divide 46 by 2
To find one of the prime factors, we divide 46 by 2:
$$ 46 \div 2 = 23 $$
Thus, we have found that one of the prime factors is 2.
- Check if the result (23) is a prime number
Next, we need to check if 23 is a prime number. A prime number has no divisors other than 1 and itself. The factors of 23 are only 1 and 23.
- Conclude the factorization
Since we have 2 as a prime factor and 23 is also a prime number, the complete prime factorization of 46 is:
$$ 46 = 2 \times 23 $$
The prime factorization of 46 is $2 \times 23$.
More Information
Prime factorization is useful for understanding the building blocks of numbers. Both 2 and 23 are prime numbers, and this breakdown can help in various areas of mathematics, including simplifications and finding common factors.
Tips
- A common mistake is forgetting to check if the resulting quotient (23) is prime after dividing by 2. Always verify the primality of the result.
- Another mistake is dividing by the wrong number. Since 46 is even, always start with 2.
