Is 1488 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 1488 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 1488 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 1488 is prime or composite.

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

Step 2: Divide 1488 by 2. It is divisible by 2, so 2 is a factor of 1488.

Step 3: Divide 1488 by 3. It is divisible by 3, so 3 is a factor of 1488.

Step 4: You can simplify checking divisors up to 1488 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1488 by numbers like 2, 3, 4, etc., we find multiple divisors.

Since 1488 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 8. Eight is an even number, which means that 1488 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1488 is 21. Since 21 is divisible by 3, 1488 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 1488 is not divisible by 5.

Divisibility by 7: The last digit in 1488 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Subtract it from the rest of the number (148 - 16 = 132). Since 132 is divisible by 7, 1488 is also divisible by 7.

Divisibility by 11: In 1488, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 16. Their difference is 7, which is not divisible by 11. Thus, 1488 is not divisible by 11.

Since 1488 is divisible by several numbers, 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 up to a certain range 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, you will have a list of prime numbers in a given range.

Since 1488 is not present in the list of prime numbers, 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 1488 as 2 × 744.

Step 2: In 2 × 744, 744 is a composite number. Break 744 further into 2 × 372.

Step 3: Continue factorizing until only prime numbers remain. Eventually, 1488 can be expressed as 2 × 2 × 2 × 2 × 3 × 31.

Hence, the prime factorization of 1488 is 2^4 × 3 × 31.

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

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.

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

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

• Prime factorization: The process of expressing a number as the product of its prime factors.