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What is the prime factorization of 1200?
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To calculate the prime factors of 1200 enter a number in the field below and press decompose:
Answer to the Factorization of 1200
The factorization of 1200 is equal to 2 × 2 × 2 × 2 × 3 × 5 × 5. We find these factors by successively dividing 1200 by the prime numbers until we obtain the prime factors.
Factor Tree of 1200
The prime factor tree of 1200 is an illustration that shows how the number 1200 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:
| 1200 | |||||||||||
| 2 | 600 | ||||||||||
| 2 | 300 | ||||||||||
| 2 | 150 | ||||||||||
| 2 | 75 | ||||||||||
| 3 | 25 | ||||||||||
| 5 | 5 | ||||||||||
Steps to Factor the Number 1200
1. Division by Smaller Prime Numbers:
Start by dividing the number 1200 by the smallest prime numbers, starting with the smallest prime, which is 2.
1200 ÷ 2 = 600
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.
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
3. Obtenção dos Fatores Primos:
Now, the numbers by which you divided 1200 and got integer results are the prime factors of 1200. In this case, we have 2, 2, 2, 2, 3, 5 and 5.
4. Expressão da Fatoração:
Write the factorization of the number 1200 using its prime factors. The full factorization of 1200 is:
1200 = 2 × 2 × 2 × 2 × 3 × 5 × 5
These steps show how the number 1200 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.
