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What is the prime factorization of 256?

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To calculate the prime factors of 256 enter a number in the field below and press decompose:

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Answer to the Factorization of 256

The factorization of 256 is equal to 2⁸. We find these factors by successively dividing 256 by the prime numbers until we obtain the prime factors.

Factor Tree of 256

The prime factor tree of 256 is an illustration that shows how the number 256 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:

	256

2		128

	2		64

		2		32

			2		16

				2		8

					2		4

						2		2

Steps to Factor the Number 256

1. Division by Smaller Prime Numbers:

Start by dividing the number 256 by the smallest prime numbers, starting with the smallest prime, which is 2.

256 ÷ 2 = 128

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.

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

3. Obtenção dos Fatores Primos:

Now, the numbers by which you divided 256 and got integer results are the prime factors of 256. In this case, we have 2 repetido 8 vezes.

4. Expressão da Fatoração:

Write the factorization of the number 256 using its prime factors. The full factorization of 256 is:

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

These steps show how the number 256 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.