Is 646 a Prime Number?

Numbers can be classified as either prime numbers or composite numbers, based on the number of factors they have.

A prime number is a natural number that is divisible only by 1 and itself. For example, 3 is a prime number because it is divisible by 1 and 3.

A composite number, on the other hand, is a positive number that has more than two factors. For example, 6 is a composite number because it is divisible by 1, 2, 3, and 6. Prime numbers have the following properties:

Prime numbers are positive numbers greater than 1.

2 is the only even prime number.

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

Any two distinct prime numbers are co-prime because they have only one common factor, which is 1.

Since 646 has more than two factors, it is not a prime number.

A prime number is characterized by having exactly two divisors: 1 and itself. Since 646 has more than two factors, it is not a prime number. Several methods can be used to determine whether a number is prime or composite, including:

• 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 check whether 646 is prime or composite.

Step 1: All numbers are divisible by 1 and themselves.

Step 2: Divide 646 by 2. It is divisible by 2, so 2 is a factor of 646.

Step 3: Divide 646 by 3. It is not divisible by 3, so 3 is not a factor of 646.

Step 4: To simplify checking, find the square root of 646 and test divisibility up to that number.

Step 5: When we divide 646 by 2, it is divisible by 2, indicating more than two divisors. Since 646 has more than 2 divisors, it is a composite number.

The divisibility test method involves using divisibility rules to check if a number is divisible by another without leaving a remainder.

Divisibility by 2: The last digit of 646 is 6, which is even, so 646 is divisible by 2.

Divisibility by 3: The sum of the digits (6 + 4 + 6 = 16) is not divisible by 3, so 646 is not divisible by 3.

Divisibility by 5: The last digit is not 0 or 5, so 646 is not divisible by 5.

Divisibility by 7: Double the last digit (6 × 2 = 12), subtract from the rest (64 - 12 = 52), and since 52 is not divisible by 7, neither is 646.

Divisibility by 11: The difference between the sum of the digits in odd positions (6 + 6 = 12) and even positions (4) is 8, which is not divisible by 11. Since 646 is divisible by 2, it has more than two factors and is therefore a composite number.

The prime number chart is created using a method known as "The Sieve of Eratosthenes." This method involves:

Step 1: Writing numbers from 1 to 100 in a grid.

Step 2: Not marking 1, as it is neither prime nor composite.

Step 3: Marking 2 as a prime number and crossing out all its multiples.

Step 4: Marking 3 as a prime number and crossing out all its multiples.

Step 5: Continuing this process until the grid is complete. By this method, we can list the prime numbers between 1 and 100. Since 646 is not on this list, it is a composite number.

Prime factorization involves breaking down a number into its prime factors and multiplying them to obtain the original number.

Step 1: We can express 646 as 2 * 323.

Step 2: In 2 * 323, 323 is a composite number. Further break down 323 into 17 * 19.

Step 3: Now we have the product consisting of only prime numbers. Hence, the prime factorization of 646 is 2 * 17 * 19.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because it has factors of 1, 2, 3, 4, 6, and 12.

• Prime numbers: Natural numbers greater than 1 with only two divisors: 1 and itself.

• Divisibility rules: Guidelines to determine if one number is divisible by another without performing division.

• Prime factorization: The process of expressing a number as the product of its prime factors.

• Co-prime numbers: Two numbers that have only one common factor, which is 1.