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 53 Prime?

Let’s determine whether (53) is a prime number by testing divisibility from the smallest primes upward.

Try dividing 53 by small primes:

  • (53 \div 2 = 26.5) → ✖️ Not divisible
  • (53 \div 3 = 17.67) → ✖️ Not divisible
  • (53 \div 4 = 13.25) → ✖️ Not divisible
  • (53 \div 5 = 10.6) → ✖️ Not divisible
  • (53 \div 6 = 8.83) → ✖️ Not divisible
  • (53 \div 7 = 7.57) → ✖️ Not divisible

Now that we’ve reached beyond (\sqrt{53} \approx 7.28), we can stop checking.

Conclusion

Since no numbers other than (1) and (53) divide evenly into 53, we conclude:

[ \boxed{53\ \text{is a prime number.}} ]

Summary

  • A prime number has exactly two factors.
  • (53) has only (1) and (53) as factors.
  • Therefore, 53 is a prime number.