Study Guides/Maths/Prime Factorization of 36
Study Guide · Maths

Prime Factorization of 36

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.

Question (Click to Flip)

How do you use prime factorization to find the square root of 36?

Answer

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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Key Facts

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.

Step-by-Step Division Method

We divide 36 by the smallest prime numbers (2, 3, 5, 7...) until we reach 1.

  1. 36 is even, so divide by 2: 36 ÷ 2 = 18
  2. 18 is even, divide by 2: 18 ÷ 2 = 9
  3. 9 is not divisible by 2. Divide by 3: 9 ÷ 3 = 3
  4. 3 is a prime number, divide by 3: 3 ÷ 3 = 1

We stop when we reach 1. The divisors are our prime factors.

The Answer

The prime factorization of 36 is: 2 × 2 × 3 × 3

In exponential form: 2² × 3²

All Factors of 36

Don't confuse prime factors with all factors.

  • Prime Factors: 2, 3
  • All Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. (Notice that 36 has an odd number of total factors because it is a perfect square: 6×6).

Questions and Answers

How do you use prime factorization to find the square root of 36?+

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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