Is 1225 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, 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 1225 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 1225 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. A few 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 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 1225 is prime or composite.

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

Step 2: Divide 1225 by 2. It is not divisible by 2, so 2 is not a factor of 1225.

Step 3: Divide 1225 by 3. It is not divisible by 3, so 3 is not a factor of 1225.

Step 4: You can simplify checking divisors up to 1225 by finding the square root. We then need to only check divisors up to the square root value. The square root of 1225 is 35.

Step 5: When we divide 1225 by 5, it is divisible by 5. Continuing this process, when we divide 1225 by 25, it is also divisible by 25.

Since 1225 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: 1225 is odd, so it is not divisible by 2. -

Divisibility by 3: The sum of the digits in the number 1225 is 10. Since 10 is not divisible by 3, 1225 is not divisible by 3. -

Divisibility by 5: The unit’s place digit is 5. Therefore, 1225 is divisible by 5. -

Divisibility by 7: 1225 divided by 7 is exactly 175. Therefore, it is divisible by 7. -

Divisibility by 11: The alternating sum of the digits in 1225 is 0 (1-2+2-5 = -4, which is not divisible by 11), so it is not divisible by 11.

Since 1225 has divisors other than 1 and itself, 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 from 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 without marking, 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 up to 100.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Since 1225 is not on the list and is greater than 100, this method involves checking numbers up to the square root of 1225, which shows that it is not a prime 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 1225 as 35 × 35.

Step 2: Break down 35 into 5 × 7.

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

Hence, the prime factorization of 1225 is 5 × 5 × 7 × 7.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 15 is a composite number because it is divisible by 1, 3, 5, and 15.

• Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6 × 6.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

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

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 8 and 9 are co-prime.