Is 247 a prime number?

Steps to Solve

1. Identify Divisors of 247

To determine if 247 is a prime number, we need to find its divisors. We can do this by checking if any natural number greater than 1 and less than 247 divides 247 evenly.

2. Check for Divisibility by Smaller Numbers

Let's check for divisibility with prime numbers less than or equal to the square root of 247. The square root of 247 is approximately 15.7, so we will check divisibility by the prime numbers 2, 3, 5, 7, 11, and 13.

3. Perform Divisibility Tests

• Divisibility by 2: 247 is odd, so it is not divisible by 2.

• Divisibility by 3: Sum of digits is $2 + 4 + 7 = 13$. Since 13 is not divisible by 3, 247 is not divisible by 3.

• Divisibility by 5: 247 does not end in 0 or 5, so it is not divisible by 5.

• Divisibility by 7: $$ 247 \div 7 \approx 35.2857 $$ Not divisible since it does not yield an integer.

• Divisibility by 11: $$ 247 \div 11 \approx 22.4545 $$ Not divisible since it does not yield an integer.

• Divisibility by 13: $$ 247 \div 13 = 19 $$ This yields an integer, which means 247 is divisible by 13.

4. Conclusion About Divisibility

Since we found that 247 has divisors other than 1 and itself (specifically, 13 and 19), it is not a prime number.