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What is the prime factorization of 420?
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To calculate the prime factors of 420 enter a number in the field below and press decompose:
Answer to the Factorization of 420
The factorization of 420 is equal to 2 × 2 × 3 × 5 × 7. We find these factors by successively dividing 420 by the prime numbers until we obtain the prime factors.
Factor Tree of 420
The prime factor tree of 420 is an illustration that shows how the number 420 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:
| 420 | |||||||||||||||||||||
| 2 | 210 | ||||||||||||||||||||
| 2 | 105 | ||||||||||||||||||||
| 3 | 35 | ||||||||||||||||||||
| 5 | 7 | ||||||||||||||||||||
Steps to Factor the Number 420
1. Division by Smaller Prime Numbers:
Start by dividing the number 420 by the smallest prime numbers, starting with the smallest prime, which is 2.
420 ÷ 2 = 210
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.
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
3. Obtenção dos Fatores Primos:
Now, the numbers by which you divided 420 and got integer results are the prime factors of 420. In this case, we have 2, 2, 3, 5 and 7.
4. Expressão da Fatoração:
Write the factorization of the number 420 using its prime factors. The full factorization of 420 is:
420 = 2 × 2 × 3 × 5 × 7
These steps show how the number 420 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.
