What is the prime factorization of 36?
Understand the Problem
The question is asking for the prime factorization of the number 36, which involves breaking it down into its prime number multipliers.
Answer
2^2 \times 3^2
Answer for screen readers
The final answer is 2^2 \times 3^2
Steps to Solve
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Determine the smallest prime factor of 36
The smallest prime number is 2. Check if 36 is divisible by 2. $$ 36 \div 2 = 18 $$
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Continue factoring the quotient
Next, check if 18 is divisible by 2. $$ 18 \div 2 = 9 $$
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Check for the next prime factor of 9
The smallest prime number for 9 is 3. Check if 9 is divisible by 3. $$ 9 \div 3 = 3 $$
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Continue factoring the quotient
Finally, check if 3 is divisible by 3. $$ 3 \div 3 = 1 $$
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List all prime factors
Combine all the factors to write out the prime factorization. $$ 36 = 2 \times 2 \times 3 \times 3 $$ This can also be written as $$ 36 = 2^2 \times 3^2 $$
The final answer is 2^2 \times 3^2
More Information
Prime factorization expresses a number as a product of its prime factors. The prime factorization helps in many areas, such as simplifying fractions and finding the greatest common divisors and least common multiples.
Tips
A common mistake is stopping the factorization process too early or missing prime factors. Ensure that all factors are primes.
