To find the prime factorization of 27,000, we will break it down step by step by dividing the number by its smallest prime factors:

1. Start by dividing by 2 (the smallest prime number):
   \[
   27000 \div 2 = 13500
   \]
   \[
   13500 \div 2 = 6750
   \]
   \[
   6750 \div 2 = 3375
   \]
   Since 3375 is odd, we now move to the next smallest prime, which is 3.

2. Divide by 3:
   \[
   3375 \div 3 = 1125
   \]
   \[
   1125 \div 3 = 375
   \]
   \[
   375 \div 3 = 125
   \]
   125 is not divisible by 3, so we move to the next prime number, which is 5.

3. Divide by 5:
   \[
   125 \div 5 = 25
   \]
   \[
   25 \div 5 = 5
   \]
   \[
   5 \div 5 = 1
   \]

Thus, the prime factorization of 27,000 is:
\[
2^3 \times 3^3 \times 5^3


Learn how to find the prime factorization of 27,000 with a detailed step-by-step solution. This problem involves dividing by prime numbers like 2, 3, and 5, and is suitable for students in Grades 6-8. Understand key number theory concepts such as the Fundamental Theorem of Arithmetic.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation