Express the prime factorization of 84 with exponents
The prime factorization of 84 can be expressed as 2^2 * 3^1 * 7^1.
well actaully the correct answer choice for me is 2^2*3*7
You are correct! The prime factorization of 84 can also be expressed as 2^2 * 3 * 7. Thank you for pointing that out!
To express the prime factorization of a number with exponents, we need to find all the prime numbers that can divide the given number and their corresponding exponents.
To find the prime factorization of 84, we can start by dividing it by the smallest prime number, which is 2. If 84 is divisible by 2, we continue dividing until it is no longer divisible by 2.
84 ÷ 2 = 42
Now, we repeat the process with the new quotient, which is 42. Since 42 is still divisible by 2, we continue dividing.
42 ÷ 2 = 21
Again, we continue the process with 21, which is still divisible by 2.
21 ÷ 2 = 10.5
At this point, we see that 10.5 is not a whole number, so we move to the next prime number, which is 3. We divide 21 by 3.
21 ÷ 3 = 7
Now, we have reached a prime number. 7 cannot be divided any further.
To summarize the steps:
1. Divide the given number (84) by the smallest prime number (2) and keep dividing until it is no longer divisible.
2. Repeat the process with the new quotient until it becomes a prime number.
In the case of 84, the prime factorization is:
84 = 2^2 × 3 × 7