Quelle est la décomposition en facteurs premiers de 459 ?
Understand the Problem
La question demande quelle est la décomposition en produit de facteurs premiers du nombre 459. Il faut donc trouver les nombres premiers qui, multipliés ensemble, donnent 459.
Answer
$3 \times 3 \times 3 \times 17$
Answer for screen readers
$3 \times 3 \times 3 \times 17$
Steps to Solve
- Check if 459 is divisible by 3
To check if 459 is divisible by 3, we add up its digits: $4 + 5 + 9 = 18$. Since 18 is divisible by 3, 459 is also divisible by 3. $459 \div 3 = 153$
- Check if 153 is divisible by 3
To check if 153 is divisible by 3, we add up its digits: $1 + 5 + 3 = 9$. Since 9 is divisible by 3, 153 is also divisible by 3. $153 \div 3 = 51$
- Check if 51 is divisible by 3
To check if 51 is divisible by 3, we add up its digits: $5 + 1 = 6$. Since 6 is divisible by 3, 51 is also divisible by 3. $51 \div 3 = 17$
- Check if 17 is a prime number
17 is a prime number because its only divisors are 1 and itself.
- Write the prime factorization of 459
The prime factorization of 459 is therefore $3 \times 3 \times 3 \times 17$.
$3 \times 3 \times 3 \times 17$
More Information
Prime factorization is the process of breaking down a number into its prime factors, which are prime numbers that, when multiplied together, equal the original number.
Tips
A common mistake is to stop factoring too early and include composite numbers in the final answer. Also, not knowing the divisibility rules can make factorization time-consuming.
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