Is 901 a Prime Number?

There are two types of numbers, mainly — 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, 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.
• Since 901 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 901 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. Some of the methods are: -

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 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 901 is prime or composite.

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

Step 2: Divide 901 by 2. It is not divisible by 2, so 2 is not a factor of 901.

Step 3: Divide 901 by 3. The sum of the digits (9 + 0 + 1 = 10) is not divisible by 3, so 3 is not a factor of 901.

Step 4: Continue this process, testing divisibility by 5, 7, etc.

Step 5: When we divide 901 by 17, it is divisible by 17 (901 ÷ 17 = 53).

Since 901 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: The number in the ones' place value is 1. Since 1 is not even, 901 is not divisible by 2. -

Divisibility by 3: The sum of the digits in the number 901 is 10. Since 10 is not divisible by 3, 901 is not divisible by 3. -

Divisibility by 5: The unit’s place digit is 1. Therefore, 901 is not divisible by 5. -

Divisibility by 7: Testing further divisibility, 901 is not divisible by 7 or 11. -

Divisibility by 17: 901 is divisible by 17 (901 ÷ 17 = 53).

Since 901 is divisible by 17, 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 numbers in sequence, typically 1 to 100.

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. Numbers that are not crossed are prime. Through this process, we will have a list of prime numbers within the range.

Since 901 is not found in the list of primes and is divisible by 17, 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 901 as 17 × 53.

Step 2: Both 17 and 53 are prime numbers.

Step 3: Thus, the prime factorization of 901 is 17 × 53, confirming it is not a prime number.

• Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than two numbers.

• Divisibility Test: A quick way to determine whether one number is divisible by another.

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

• Prime Factorization: Expressing a number as the product of its prime factors.