What is the prime factorization of 126 using exponents?

To find the prime factorization of 126 using exponents, we start by dividing the number by the smallest prime number, which is 2.

126 ÷ 2 = 63

Now we have 2 as one of the prime factors. Next, we need to factor 63. The smallest prime number that can divide 63 is 3.

63 ÷ 3 = 21

Next, we take 21 and again divide by 3 since it’s the smallest prime factor.

21 ÷ 3 = 7

Now, we see that 7 is a prime number, so we cannot factor it any further.

Putting it all together, we have:

• 2 from the division by 2
• 3 twice from the two divisions by 3
• 7 from the final division

Thus, the prime factorization of 126 can be expressed as:

2¹ × 3² × 7¹