Yes, you can use the prime factorization of a number to determine whether it is even or odd.
Every integer can be expressed as a product of prime factors. If a number is even, it means it is divisible by 2. In the prime factorization of an even number, there will always be at least one factor of 2.
On the other hand, if a number is odd, it means it is not divisible by 2. In the prime factorization of an odd number, there will be no factors of 2.
Let's consider a few examples:
Example 1: Prime factorization of 24
The prime factorization of 24 is 2×2×2×3. As we can see, there are three factors of 2 in the prime factorization, indicating that 24 is even.
Example 2: Prime factorization of 17
The prime factorization of 17 is 17 itself. There are no factors of 2 in the prime factorization, indicating that 17 is odd.
Example 3: Prime factorization of 36
The prime factorization of 36 is 2×2×3×3. Again, there are two factors of 2 in the prime factorization, indicating that 36 is even.
By analyzing the prime factorization and checking if there are any factors of 2, one can easily determine whether a number is even or odd.
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