Is 913 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, 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 like:

• 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 913 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 913 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. 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 913 is prime or composite.

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

Step 2: Divide 913 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 913 by 3. The sum of its digits (9 + 1 + 3 = 13) is not divisible by 3, so 913 is not divisible by 3.

Step 4: You can simplify checking divisors up to 913 by finding the square root value. We then need to only check divisors up to the approximate square root value, which is about 30.2.

Step 5: When we divide 913 by 11 (913 ÷ 11 = 83), it is divisible by 11.

Since 913 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. It is called the Divisibility Test Method.

Divisibility by 2: 913 is not divisible by 2, as it is an odd number.

Divisibility by 3: The sum of the digits in the number 913 is 13, which is not divisible by 3. Divisibility by 5: The unit’s place digit of 913 is 3, so it is not divisible by 5.

Divisibility by 7: Double the last digit (3 × 2 = 6) and subtract it from the rest of the number (91 - 6 = 85). Since 85 is not divisible by 7, 913 is also not divisible by 7.

Divisibility by 11: In 913, the difference between the sum of the digits in odd positions (9 + 3 = 12) and even positions (1) is 11, which is divisible by 11, so 913 is divisible by 11.

Since 913 is divisible by 11, it has more than two factors. Therefore, it is 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 1 to 1000 in rows and columns.

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 reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 1000.

913 is not present in the list of prime numbers, so 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 913 as 11 × 83.

Step 2: Both 11 and 83 are prime numbers.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 913 is 11 × 83.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 913 is a composite number because it is divisible by 1, 11, 83, and 913.

• Divisibility rules: A set of guidelines to determine if one number is divisible by another without performing division.

• Prime factorization: The expression of a number as a product of its prime factors. For example, 913 = 11 × 83.

• Odd numbers: Numbers not divisible by 2. For example, 913 is an odd number.

• Prime numbers: Natural numbers greater than 1 with only two distinct positive divisors: 1 and themselves. For example, 11 is a prime number.