The prime factorization of 63 is expressed as 3² × 7.
To find the prime factorization, we start by dividing 63 by the smallest prime number, which is 2. Since 63 is odd, we move to the next prime number, 3. Dividing 63 by 3 gives us 21:
- 63 ÷ 3 = 21
Next, we continue factoring 21. We can again divide by 3:
- 21 ÷ 3 = 7
Now, we have 7, which is also a prime number. Therefore, we can stop here. Collecting our factors, we have:
- 63 = 3 × 3 × 7
Using exponents, we represent the repeated factor (which is 3) as 3². Thus, the complete prime factorization of 63 using exponents is:
- 3² × 7