Is 371 prime?
Understand the Problem
The question is asking whether the number 371 is a prime number. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. To determine if 371 is prime, we will check if it has any divisors other than 1 and itself.
Answer
371 is not a prime number.
Answer for screen readers
The number 371 is not a prime number.
Steps to Solve
- Determine the range for testing divisibility
To check if 371 is a prime number, we should test for divisors up to the square root of 371. The square root of 371 is approximately 19.2. Therefore, we will test for divisibility using the prime numbers less than or equal to 19: 2, 3, 5, 7, 11, 13, 17, and 19.
- Check divisibility by 2
Since 371 is an odd number, it is not divisible by 2.
- Check divisibility by 3
To check divisibility by 3, we can sum the digits of 371:
$$ 3 + 7 + 1 = 11 $$
Since 11 is not divisible by 3, 371 is also not divisible by 3.
- Check divisibility by 5
Since 371 does not end in 0 or 5, it is not divisible by 5.
- Check divisibility by 7
Now we divide 371 by 7:
$$ 371 \div 7 \approx 53 $$
Since 53 is a whole number, 371 is divisible by 7.
- Conclusion
Since we found that 371 can be divided by 7, it means it has divisors other than 1 and itself. Thus, 371 is not a prime number.
The number 371 is not a prime number.
More Information
371 can be expressed as the product of two smaller numbers: ( 371 = 7 \times 53 ). This demonstrates that prime numbers can only be divided evenly by 1 and themselves.
Tips
A common mistake is to only check divisibility by small numbers or to stop checking too early. Always ensure to check up to the square root of the number for thorough testing.