Is 1763 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 have 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 1763 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 1763 has more than two factors, it is not a prime number. Some methods are used to distinguish between prime and composite numbers, such as:

• 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 numbers as prime or composite.

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 1763 is prime or composite.

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

Step 2: Divide 1763 by 2. It is not divisible by 2, so 2 is not a factor of 1763.

Step 3: Divide 1763 by 3. It is not divisible by 3, so 3 is not a factor of 1763.

Step 4: Continue checking divisibility by subsequent numbers up to the square root of 1763.

Step 5: When we divide 1763 by 37, it is divisible, so 37 is a factor of 1763. Since 1763 has more than two 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: 1763 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1763 is 17. Since 17 is not divisible by 3, 1763 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 1763 is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 1763 is divisible because 1763/7 = 251.

Divisibility by 11: The alternating sum of the digits in 1763 is 5. Since 5 is not divisible by 11, 1763 is not divisible by 11. Since 1763 is divisible by 37 and 7, it has more than two factors. Therefore, 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 1 to 100 in 10 rows and 10 columns.

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

Step 3: Mark 2 as a prime number and cross out all multiples of 2.

Step 4: Mark 3 as a prime number and cross out all multiples of 3.

Step 5: Repeat this process until you reach numbers consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100. Since 1763 is not in this list, and is divisible by other numbers like 37 and 7, it is not a prime number.

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

Step 1: We can write 1763 as 37 x 47.

Step 2: Both 37 and 47 are prime numbers, so the prime factorization of 1763 is 37 x 47.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1763 is a composite number because it is divisible by 1, 37, 47, and 1763.

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

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1763 is 37 x 47.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

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