Write 28 as a product of prime factors.
Understand the Problem
The question is asking for the prime factorization of the number 28. To solve this, we will break down 28 into its prime factors, starting by dividing it by the smallest prime number and continuing until we can no longer divide.
Answer
The prime factorization of 28 is $2^2 \times 7$.
Answer for screen readers
The prime factorization of 28 is $2^2 \times 7$.
Steps to Solve
- Start with the number 28
We begin with 28 and look for the smallest prime number that can divide it. The smallest prime number is 2.
- Divide by the smallest prime number
We divide 28 by 2: $$ 28 \div 2 = 14 $$
- Repeat division with 2
Next, we divide 14 by 2 again: $$ 14 \div 2 = 7 $$
- Check if the result is prime
Now we have 7, which is a prime number. Since 7 cannot be divided by any other prime numbers, we can stop here.
- List the prime factors
We found that: $$ 28 = 2 \times 2 \times 7 $$ or in exponent form, $$ 28 = 2^2 \times 7^1 $$
The prime factorization of 28 is $2^2 \times 7$.
More Information
The number 28 is made up of the prime factors 2 and 7, where 2 appears twice. Prime factorization is important in many areas of mathematics, including number theory and simplifying fractions.
Tips
Some common mistakes include:
- Forgetting to test if the last result is a prime number.
- Dividing by a non-prime number instead of the smallest prime.
- Overlooking the need to express the factors in proper prime factorization format.