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What is the prime factorization of 512?

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Answer to the Factorization of 512

The factorization of 512 is equal to 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. We find these factors by successively dividing 512 by the prime numbers until we obtain the prime factors.

Factor Tree of 512

The prime factor tree of 512 is an illustration that shows how the number 512 is decomposed into its fundamental prime factors, as 2, 3 and 5. This visual representation helps you understand the underlying structure of the number and how it is formed from smaller prime numbers.

Look at the following tree:

	512

2		256

	2		128

		2		64

			2		32

				2		16

					2		8

						2		4

							2		2

Steps to Factor the Number 512

1. Division by Smaller Prime Numbers:

Start by dividing the number 512 by the smallest prime numbers, starting with the smallest prime, which is 2.

512 ÷ 2 = 256

2. Continuação das Divisões:

Agora, continue dividindo o resultado da etapa anterior por números primos menores, até que não seja mais possível fazer divisões inteiras.

256 ÷ 2 = 128

128 ÷ 2 = 64

64 ÷ 2 = 32

3. Obtenção dos Fatores Primos:

Now, the numbers by which you divided 512 and got integer results are the prime factors of 512. In this case, we have 2 repetido 9 vezes.

4. Expressão da Fatoração:

Write the factorization of the number 512 using its prime factors. The full factorization of 512 is:

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

These steps show how the number 512 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.

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