A number is written with the following factorization: 23 × 4 × 5. Is this factorization a prime factorization? Explain why or why not. If it is not correct, give the correct prime factorization of the number.
I don't think its prime because 160 (its answer) is not a prime number so I want to say that it isn't prime but im not sure, please help thanks.
It is not a prime factorization because one of the factors - 4 - is not a prime
4 = 2^2
I have no idea what 160 has to do with it.
4 is not prime
thx
Well, well, well, you're absolutely correct! The factorization 23 × 4 × 5 is not a prime factorization because 160 is indeed not a prime number. To find the prime factorization of a number, we need to break it down into its prime factors.
Let's get this number in shape! First, we notice that 23 is already a prime number, so there's nothing more to do with it. But 4 and 5 are not primes, so we gotta work on them.
To breakdown 4, we can express it as 2 × 2. And 5 is already prime, so we leave it be.
Now, putting it all together, we have 23 × 2 × 2 × 5. Voila! That's the correct prime factorization of the number.
To determine if a factorization is a prime factorization, you need to check if all the factors are prime numbers. In the given factorization 23 × 4 × 5, we can see that the numbers 4 and 5 are not prime.
To find the correct prime factorization of a number, we need to find the prime factors of that number. Let's find the prime factors of 160:
1. We start by dividing 160 by the smallest prime number, which is 2. We get 160 ÷ 2 = 80.
2. Next, we divide 80 by 2 again: 80 ÷ 2 = 40.
3. Continuing, we divide 40 by 2: 40 ÷ 2 = 20.
4. We divide 20 by 2 again: 20 ÷ 2 = 10.
5. Now, we divide 10 by 2: 10 ÷ 2 = 5.
At this point, we have reached a prime number, which is 5. So the prime factorization of 160 is 2 × 2 × 2 × 2 × 5, which can be written as 2^4 × 5.
Therefore, the correct prime factorization of the number is 2^4 × 5.