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What is the prime factorization of 1600?
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To calculate the prime factors of 1600 enter a number in the field below and press decompose:
Answer to the Factorization of 1600
The factorization of 1600 is equal to 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5. We find these factors by successively dividing 1600 by the prime numbers until we obtain the prime factors.
Factor Tree of 1600
The prime factor tree of 1600 is an illustration that shows how the number 1600 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:
| 1600 | |||||||||||
| 2 | 800 | ||||||||||
| 2 | 400 | ||||||||||
| 2 | 200 | ||||||||||
| 2 | 100 | ||||||||||
| 2 | 50 | ||||||||||
| 2 | 25 | ||||||||||
| 5 | 5 | ||||||||||
Steps to Factor the Number 1600
1. Division by Smaller Prime Numbers:
Start by dividing the number 1600 by the smallest prime numbers, starting with the smallest prime, which is 2.
1600 ÷ 2 = 800
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.
800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
3. Obtenção dos Fatores Primos:
Now, the numbers by which you divided 1600 and got integer results are the prime factors of 1600. In this case, we have 2, 2, 2, 2, 2, 2, 5 and 5.
4. Expressão da Fatoração:
Write the factorization of the number 1600 using its prime factors. The full factorization of 1600 is:
1600 = 2 × 2 × 2 × 2 x 2 × 2 × 5 × 5
These steps show how the number 1600 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.
