Write the prime factor decomposition of 300 in index form.
The Correct Answer and Explanation is:
The prime factor decomposition of 300 in index form is:
300=22×3×52300 = 2^2 \times 3 \times 5^2300=22×3×52
Explanation:
To find the prime factorization of 300, we begin by dividing it by the smallest prime number, which is 2. Start by checking if 300 is divisible by 2. Since 300 is even, we divide:300÷2=150300 \div 2 = 150300÷2=150
Now, divide 150 by 2 again since it is also even:150÷2=75150 \div 2 = 75150÷2=75
At this point, 75 is no longer divisible by 2 because it is odd, so we move to the next smallest prime, which is 3. Check if 75 is divisible by 3:75÷3=2575 \div 3 = 2575÷3=25
Next, we check 25 for divisibility by 3. It is not divisible by 3, so we move on to the next prime number, 5. Divide 25 by 5:25÷5=525 \div 5 = 525÷5=5
Finally, divide 5 by 5 again:5÷5=15 \div 5 = 15÷5=1
Now, we have completely factored 300, and the prime factorization is:300=2×2×3×5×5300 = 2 \times 2 \times 3 \times 5 \times 5300=2×2×3×5×5
We can express this in index form:300=22×3×52300 = 2^2 \times 3 \times 5^2300=22×3×52
Thus, the prime factors of 300 are 2 raised to the power of 2, 3 raised to the power of 1, and 5 raised to the power of 2. The use of exponents here shows how many times each prime factor is repeated in the decomposition.
