Is 377 prime?
Understand the Problem
The question is asking whether the number 377 is a prime number or not. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. To determine if 377 is prime, we need to see if it can be divided evenly by any other numbers besides 1 and 377.
Answer
Not prime.
Answer for screen readers
377 is not a prime number.
Steps to Solve
- Identify Potential Divisors
To determine if 377 is a prime number, we need to find numbers that could be potential divisors. We will check for divisibility from 2 up to the square root of 377.
- Calculate the Square Root
Calculate the approximate square root of 377 to limit our search for divisors.
$$ \sqrt{377} \approx 19.4 $$
This means we will test for divisibility using integers up to 19.
- Test for Divisibility by Each Integer
Start dividing 377 by integers from 2 to 19.
- Check divisibility by 2 (377 is odd, so not divisible)
- Check divisibility by 3:
To check if a number is divisible by 3, add its digits (3 + 7 + 7 = 17), which is not divisible by 3.
- Check divisibility by 4 (last two digits, 77, not divisible by 4)
- Check divisibility by 5 (377 does not end in 0 or 5)
- Check divisibility by 6 (not divisible by both 2 and 3)
- Check divisibility by 7:
$$ 377 \div 7 \approx 53.857 $$ (not divisible)
Continue this process until 19.
- Identify a True Divisor
Eventually, check divisibility by 13:
$$ 377 \div 13 = 29 $$
Since 377 can be divided evenly by 13, we conclude it has divisors other than 1 and itself.
- Conclusion
Since 377 can be divided by at least one other number (13), it is not a prime number.
377 is not a prime number.
More Information
377 can be expressed as the product of 13 and 29, which confirms its status as a composite number (non-prime).
Tips
- Many might stop checking for divisibility too early, assuming a number is prime without checking all possible factors or until the square root.
- Some could miscalculate the divisibility checks or forget to check all numbers up to the square root.
