Is 1207 a Prime Number?

There are two main types of numbers — prime numbers and composite numbers, based on the number of factors. 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 itself.

A composite number is a positive number that is divisible by more than two numbers. For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow a few properties, such as:

• Prime numbers are positive numbers always 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 numbers because they have only one common factor, which is 1.
• As 1207 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1207 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, including:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization

The counting divisors method involves counting the number of divisors to determine if numbers are prime or composite. Based on the divisor count, we classify numbers as follows:

• If there is a total count of only 2 divisors, then the number is prime.
• If the count is more than 2, then the number is composite.

Let’s check whether 1207 is prime or composite.

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

Step 2: Divide 1207 by 2. It is not divisible by 2, so 2 is not a factor of 1207.

Step 3: Divide 1207 by 3. It is not divisible by 3, so 3 is not a factor of 1207.

Step 4: You can simplify checking divisors up to 1207 by finding the root value. We then need to check divisors only up to the root value.

Step 5: When we divide 1207 by 11, it is divisible. Thus, 11 is a factor of 1207.

Since 1207 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. This is called the Divisibility Test Method.

Divisibility by 2: The number in the one's place value is 7, an odd number, so 1207 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1207 is 10. Since 10 is not divisible by 3, 1207 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1207 is not divisible by 5. Divisibility by 7: Repeated division shows that 1207 is not divisible by 7.

Divisibility by 11: Alternating the sum of digits ((1 + 0) - (2 + 7) = -8), which is not divisible by 11, indicates 1207 is not divisible by 11.

Since 1207 is divisible by 11, it has more than two factors, making it a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write numbers from 1 to 1000 in a structured format.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you reach the required number range. Through this process, we have a list of prime numbers.

Since 1207 is not in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 1207 as 11 × 109.

Step 2: Both 11 and 109 are prime numbers.

Step 3: Therefore, the prime factorization of 1207 is 11 × 109.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1207 is a composite number because it is divisible by 1, 11, 109, and 1207.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 11 is a prime number.

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

• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1207 is 11 × 109.

• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 1207 are 1, 11, 109, and 1207.