What is the prime factorization of 192?
Understand the Problem
The question is asking for the prime factors of the number 192, which means we need to express 192 as a product of its prime numbers.
Answer
2^6 \times 3
Answer for screen readers
The prime factorization of 192 is $2^6 \times 3$
Steps to Solve
-
Divide 192 by the smallest prime number, 2
We start with the smallest prime number, which is 2, and keep dividing 192 until it is no longer divisible by 2.
$$ 192 \div 2 = 96 $$
- Continue dividing the quotient by 2
Next, we keep dividing the result by 2.
$$ 96 \div 2 = 48 $$ $$ 48 \div 2 = 24 $$ $$ 24 \div 2 = 12 $$ $$ 12 \div 2 = 6 $$ $$ 6 \div 2 = 3 $$
- Divide the result by the next smallest prime number
Finally, when we reach 3, it is a prime number and not divisible by 2. We divide it by itself.
$$ 3 \div 3 = 1 $$
- Write out the prime factorization
Combine all the prime factors we used.
$$ 192 = 2^6 \times 3 $$
The prime factorization of 192 is $2^6 \times 3$
More Information
Prime factorization is expressing a composite number as the product of its prime factors. The number 192 breaks down into six 2's multiplied by one 3.
Tips
Avoid stopping the factorization process too early or missing any prime factors. Always ensure the final product equals the original number when multiplied back together.
AI-generated content may contain errors. Please verify critical information
