What Is a Prime Number?

A prime number is a number that has exactly two factors:

  • (1)
  • Itself

If a number has more than two factors, it is called a composite number.

Step-by-Step: Is 57 Prime?

To test whether 57 is a prime number, try dividing it by all prime numbers up to ( \sqrt{57} \approx 7.5 ).

Step 1: Try 2

[ 57 \div 2 = 28.5 \quad \text{❌ Not divisible} ]

Step 2: Try 3

[ 57 \div 3 = 19 \quad \text{✅ Divisible} ]

Since 57 is divisible by 3, it has at least one other factor besides 1 and 57, which means:

[ \boxed{57\ \text{is not a prime number.}} ]

Conclusion

  • Prime numbers have exactly two distinct factors: (1) and the number itself.
  • (57 = 3 \times 19)
  • Therefore, 57 is a composite number.

Summary

A prime number has only two factors: (1) and itself.
Since 57 is divisible by 3 and 19, it has more than two factors.

[ \boxed{57\ \text{is not a prime number.}} ]