What are the prime factors of 46?
Understand the Problem
The question is asking for the prime factors of the number 46, which involves identifying the prime numbers that can be multiplied together to yield 46.
Answer
The prime factors of 46 are $2$ and $23$.
Answer for screen readers
The prime factors of 46 are $2$ and $23$.
Steps to Solve
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Identify the First Prime Number Start with the smallest prime number, which is 2. Check if 2 divides 46 evenly. $$ 46 \div 2 = 23 $$
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Check the Resulting Quotient After dividing, we find that 23 is the quotient. Now we need to check if 23 is a prime number.
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Determine if 23 is Prime We check if any prime numbers (up to the square root of 23) divide 23 without a remainder. The prime numbers less than or equal to 5 (since $5^2 = 25 > 23$) are 2, 3, and 5.
- Dividing by 2: 23 is not even, so not divisible.
- Dividing by 3: $23 \div 3$ does not yield an integer.
- Dividing by 5: $23 \div 5$ also does not yield an integer.
Since 23 is not divisible by any of these, it is a prime number.
- Combine the Prime Factors We can now state that the prime factorization of 46 is the product of the two prime numbers found: $$ 2 \times 23 $$
The prime factors of 46 are $2$ and $23$.
More Information
The number 46 is not a prime number itself because it can be divided by other numbers (in this case, 2 and 23). Understanding prime factorization helps in various areas of mathematics, including simplifying fractions and finding the greatest common divisor.
Tips
- Confusing composite numbers with prime numbers: Remember that prime numbers only have two factors, 1 and themselves.
- Not checking all relevant prime numbers to determine the primality of a quotient.
