Final answer:
The prime decomposition of 285 is the multiplication of its prime factors, which are 3, 5, and 19. You can find these factors by dividing 285 by the smallest prime numbers until all factors are prime.
Step-by-step explanation:
Prime Decomposition of 285
The prime decomposition of a number is expressing it as a product of its prime factors. To find the prime decomposition of 285, we start with the smallest prime number, which is 2. However, since 285 is an odd number it cannot be divided evenly by 2, so the next smallest prime number is 3. We check if 285 is divisible by 3 and find that it is not, as 3 x 95 equals 285. Thus, 3 is one of the prime factors. Now we have 285 divided by 3 which is 95, and we need to find the prime factors of 95. Since 95 is not divisible by 2 or 3, we move on to the next prime number, which is 5. We find that 95 is divisible by 5 (5 x 19 is 95). This leaves us with 19, which is also a prime number.
The prime decomposition of 285 is therefore 3 x 5 x 19.
This method of prime factorization can be used for decomposing any composite number into its prime constituents, ensuring that each factor is a prime number and there are no further divisible prime numbers within the set. Remember, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. By identifying and dividing by prime numbers starting from the smallest, we systematically break down the original number into its basic prime elements.