What is the prime factorization of 729?

Solution:

Prime factorization is a method of expressing a number as a product of its prime factors.

The fundamental theorem of arithmetic says that any composite number can be expressed in a unique way as a product of its prime factors.

729 is a perfect square number. It is (27)²

27 can also be written as  3 × 3 × 3

Therefore, 729 = (3 × 3 × 3)² which is (3³)²  = 3⁶ in the exponent form.

Thus, the prime factorization of 729 is 3⁶ which is 3 × 3 × 3 × 3 × 3 × 3.

What is the prime factorization of 729?

Summary:

The prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3