Prime factorization is the process of breaking down a composite number into a product of prime numbers. Finding the prime factorization of 36 is a common foundational math problem.
A number's prime factorization is like its unique DNA. The Fundamental Theorem of Arithmetic states that every integer greater than 1 has a unique prime factorization.
We divide 36 by the smallest prime numbers (2, 3, 5, 7...) until we reach 1.
We stop when we reach 1. The divisors are our prime factors.
The prime factorization of 36 is: 2 × 2 × 3 × 3
In exponential form: 2² × 3²
Don't confuse prime factors with all factors.
Look at the prime factorization: 2² × 3². To find the square root, halve the exponents: 2¹ × 3¹ = 2 × 3 = **6**. So, √36 = 6.
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