Is the number 57 prime or composite? A prime B composite
The Correct Answer and Explanation is:
The correct answer is B composite.
A composite number is a positive integer greater than 1 that has more than two distinct positive divisors (i.e., it can be factored into smaller positive integers). In contrast, a prime number has exactly two distinct positive divisors: 1 and itself.
Let’s break down 57:
- Divisibility check: Start by checking if 57 is divisible by smaller primes, such as 2, 3, 5, 7, and so on.
- Divisibility by 2: 57 is odd, so it is not divisible by 2.
- Divisibility by 3: To check divisibility by 3, sum the digits of 57: 5+7=125 + 7 = 125+7=12. Since 12 is divisible by 3, 57 is divisible by 3.
- Dividing 57 by 3 gives 57÷3=1957 ÷ 3 = 1957÷3=19.
- Factoring: We found that 57 can be factored as 57=3×1957 = 3 × 1957=3×19. Since 57 has divisors other than 1 and itself (specifically 3 and 19), it is a composite number.
Thus, 57 is a composite number because it has more than two divisors: 1, 3, 19, and 57.
In summary, prime numbers only have divisors of 1 and the number itself, whereas composite numbers have more divisors. Since 57 can be factored into 3 and 19, it is composite.
