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What is the prime factorization of 180?
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To calculate the prime factors of 180 enter a number in the field below and press decompose:
Answer to the Factorization of 180
The factorization of 180 is equal to 2 × 2 × 3 × 3 × 5. We find these factors by successively dividing 180 by the prime numbers until we obtain the prime factors.
Factor Tree of 180
The prime factor tree of 180 is an illustration that shows how the number 180 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:
| 180 | |||||||||||
| 2 | 90 | ||||||||||
| 3 | 30 | ||||||||||
| 2 | 15 | ||||||||||
| 5 | 3 | ||||||||||
Steps to Factor the Number 180
1. Division by Smaller Prime Numbers:
Start by dividing the number 180 by the smallest prime numbers, starting with the smallest prime, which is 2.
180 ÷ 2 = 90
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.
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
3. Continuação das Divisões:
Continue as divisões até não ser mais possível obter divisões inteiras.
5 ÷ 5 = 1
4. Obtenção dos Fatores Primos:
Now, the numbers by which you divided 180 and got integer results are the prime factors of 180. In this case, we have 2, 2, 3, 3 and 5.
5. Expressão da Fatoração:
Write the factorization of the number 180 using its prime factors. The full factorization of 180 is:
180 = 2 × 2 × 3 × 3 × 5
These steps show how the number 180 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.
