57 prime or composite
The Correct Answer and Explanation is:
The number 57 is composite.
A composite number is a positive integer that has more than two distinct positive divisors, which means it can be divided by numbers other than 1 and itself. In contrast, a prime number has exactly two distinct positive divisors: 1 and itself.
To determine whether 57 is prime or composite, we need to check if it has divisors other than 1 and 57. Begin by checking for divisibility by smaller prime numbers like 2, 3, 5, and 7.
- Divisibility by 2: 57 is odd, so it is not divisible by 2.
- Divisibility by 3: Sum the digits of 57 (5 + 7 = 12). Since 12 is divisible by 3, 57 is divisible by 3. Dividing 57 by 3 gives 19.
Now, we know that 57 = 3 × 19, where 19 is a prime number. Therefore, 57 is a composite number because it can be factored into smaller positive integers (3 and 19) other than 1 and itself.
In conclusion, 57 is not a prime number but a composite number because it has divisors other than 1 and 57. Its prime factorization is 3 × 19.
