Is 387 a Prime Number?

Numbers can be classified as either prime or composite based on their factors. A prime number is a natural number greater than 1 that is divisible only by 1 and itself.

For example, 3 is a prime number because it has only two divisors: 1 and 3.

A composite number has more than two divisors.

For instance, 6 is composite because it has divisors 1, 2, 3, and 6.

Key properties of prime numbers include:

Prime numbers are greater than 1.

2 is the only even prime number.

They have exactly two factors: 1 and the number itself.

Two distinct prime numbers are co-prime as their only common factor is 1.

Since 387 has more than two factors, it is not a prime number.

A prime number has exactly two divisors: 1 and itself. Since 387 has more than two factors, it is not a prime number. Several methods can be employed to distinguish between prime and composite numbers:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The counting divisors method involves counting the number of divisors a number has to determine if it is prime or composite.

If a number has exactly 2 divisors, it is prime.

If it has more than 2 divisors, it is composite.

Let's verify whether 387 is prime or composite:

Step 1: Every number is divisible by 1 and itself.

Step 2: Check divisibility of 387 by 2. Since 387 is odd, it is not divisible by 2.

Step 3: Divide 387 by 3. The sum of the digits (3 + 8 + 7) is 18, which is divisible by 3, so 3 is a factor.

Step 4: Check divisibility by other numbers up to the square root of 387. Since 387 has more than 2 divisors, it is a composite number.

We use divisibility rules to determine if a number is divisible by another number without a remainder: - Divisibility by 2: 387 is odd, so it is not divisible by 2.

Divisibility by 3: The digit sum of 387 is 18, which is divisible by 3, so 387 is divisible by 3.

Divisibility by 5: The last digit of 387 is not 0 or 5, so it is not divisible by 5.

Divisibility by 7: Double the last digit (7 × 2 = 14), then subtract from the rest (38 - 14 = 24). Since 24 is divisible by 7, 387 is divisible by 7.

Divisibility by 11: The alternating sum of digits (3 - 8 + 7 = 2) is not divisible by 11. Since 387 has more than two factors.

it is a composite number.

The prime number chart is a tool created using the Sieve of Eratosthenes:

1. List numbers from 1 to 100 in rows and columns.

2. Leave 1 unmarked as it is neither prime nor composite.

3. Mark 2 and cross out multiples of 2.

4. Mark 3 and cross out multiples of 3.

5. Continue until all primes are marked. From this process, we find that 387 is not in the list of prime numbers, confirming it is a composite number.

Prime factorization involves expressing a number as a product of prime factors:

1. Start with 387.

2. Divide by the smallest prime, 3: 387 ÷ 3 = 129.

3. Divide 129 by 3 again: 129 ÷ 3 = 43.

4. 43 is a prime number.

Thus, the prime factorization of 387 is 3 × 3 × 43.

• Composite numbers: Natural numbers greater than 1 that have more than two divisors. Example: 12, with divisors 1, 2, 3, 4, 6, and 12.

• Prime numbers: Natural numbers greater than 1 with exactly two distinct divisors: 1 and itself. Example: 7. 

• Divisibility: A number is divisible by another if the remainder is zero when divided.

• Factors: Numbers that divide another number completely. Example: Factors of 4 are 1, 2, and 4.

• Prime factorization: Expressing a number as a product of its prime factors. Example: 20 is 2 × 2 × 5.