How do you write the prime factorization of 28?

To find the prime factorization of 28, we need to break it down into its prime factors. Prime factors are the prime numbers that multiply together to give the original number. Let's go through the steps to find the prime factorization of 28.

Step-by-Step Breakdown

Identifying the Smallest Prime Factor

We start by dividing 28 by the smallest prime number, which is 2. Since 28 is even, it is divisible by 2.

• 28 ÷ 2 = 14

Continuing the Factorization

Now we take the quotient, which is 14, and repeat the process. Again, 14 is even and divisible by 2.

• 14 ÷ 2 = 7

Identifying the Last Factor

Now we have 7, which is a prime number itself. Since we cannot factor 7 any further, we stop here.

Putting It All Together

The prime factorization of 28 can now be expressed as the product of its prime factors:

• 28 = 2 × 2 × 7

To make it clearer, we can also write this using exponents:

• 28 = 2² × 7

Visualizing the Process

Think of prime factorization like breaking down a recipe into its simplest ingredients. Just as you would identify the basic components of a dish, prime factorization helps us understand the fundamental building blocks of a number.

Why Prime Factorization Matters

Understanding prime factorization is essential in various areas of mathematics, including simplifying fractions, finding the greatest common divisor (GCD), and working with least common multiples (LCM). It also plays a crucial role in number theory and cryptography.

In summary, the prime factorization of 28 is 2² × 7, which shows how we can express the number as a product of its prime factors. This method can be applied to any whole number to uncover its prime components.