What is the prime factorization of 300 using exponents?

The prime factorization of 300 is expressed as 2² × 3¹ × 5².

To explain further, we start by finding the prime factors of 300. We can do this by dividing 300 by the smallest prime number, which is 2:

• 300 ÷ 2 = 150
• 150 ÷ 2 = 75

At this point, 75 cannot be divided by 2 anymore. We then move to the next prime number, which is 3:

• 75 ÷ 3 = 25

Next, we divide 25 by the next prime number, which is 5:

• 25 ÷ 5 = 5
• 5 ÷ 5 = 1

Now we compile all the prime factors we used:

• Prime factor 2 appears twice (2 × 2)
• Prime factor 3 appears once (3)
• Prime factor 5 appears twice (5 × 5)

This gives us the prime factorization in exponent form: 2² × 3¹ × 5².