Let's find the prime factors of 240 using a factor tree. This method involves breaking down the number into smaller factors until all factors are prime numbers.
1. Start with the number 240. We can divide it by the smallest prime number, which is 2.
[tex]\[ 240 \div 2 = 120 \][/tex]
2. Now we have 120. Divide 120 by 2 again.
[tex]\[ 120 \div 2 = 60 \][/tex]
3. Next, take the 60 and divide it by 2.
[tex]\[ 60 \div 2 = 30 \][/tex]
4. Continue dividing by 2.
[tex]\[ 30 \div 2 = 15 \][/tex]
5. Now, 15 is not evenly divisible by 2. The next smallest prime number is 3.
[tex]\[ 15 \div 3 = 5 \][/tex]
6. Finally, 5 is a prime number.
Now we can list out all the factors we used:
[tex]\[ 2, 2, 2, 2, 3, 5 \][/tex]
So, the prime factorization of 240 is:
[tex]\[ 2 \times 2 \times 2 \times 2 \times 3 \times 5 \][/tex]
Thus, the expression that shows the prime factorization is:
[tex]\[ D. \, 2 \times 2 \times 2 \times 2 \times 3 \times 5 \][/tex]
