Is 1012 a Prime Number?

There are two types of numbers, mostly — Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself. For example, 7 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, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Prime numbers have 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 1012 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 1012 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, including:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers.

If there is a total count of only 2 divisors, then the number would be prime.

If the count is more than 2, then the number is composite. Let’s check whether 1012 is prime or composite.

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

Step 2: Divide 1012 by 2. It is divisible by 2, so 2 is a factor of 1012.

Step 3: Divide 1012 by 3. It is not divisible by 3, so 3 is not a factor of 1012.

Step 4: We can simplify checking divisors up to 1012 by finding the square root value. We then need to check divisors up to the square root value. Since 1012 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. It is called the Divisibility Test Method.

Divisibility by 2: The number 1012 ends with an even digit (2), so it is divisible by 2.

Divisibility by 3: The sum of the digits in 1012 is 4 (1 + 0 + 1 + 2), which is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1012 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (2 × 2 = 4), and subtract it from the rest of the number (101 - 4 = 97). Since 97 is not divisible by 7, 1012 is not divisible by 7.

Divisibility by 11: In 1012, the sum of the digits in odd positions is 2, and the sum of the digits in even positions is 1. The difference is not a multiple of 11, so 1012 is not divisible by 11. Since 1012 has factors other than 1 and itself, it is a composite number.

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

Step 1: Write numbers sequentially.

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 the multiples of 2.

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

Step 5: Repeat this process until you complete the list. Through this process, we can list prime numbers. Since 1012 is not listed as a prime number, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 1012 as 2 × 506.

Step 2: In 2 × 506, 506 is a composite number. Further, break 506 into 2 × 253.

Step 3: Now, break 253 into 11 × 23. Step 4: The prime factorization of 1012 is 2 × 2 × 11 × 23.

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

• Twin primes: A pair of prime numbers whose difference is 2 are called twin prime numbers. For example, (11, 13) is a pair of twin primes because the difference between 13 and 11 is 2.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

• Divisibility: A property determining if a number can be divided by another without leaving a remainder. For example, 10 is divisible by 2.

• Prime number: A natural number greater than 1 with no divisors other than 1 and itself. For example, 5 is a prime number.