Is 1387 a Prime Number?
2026-02-28 01:46 Diff
https://brightchamps.com/en-us/math/numbers/is-1387-a-prime-number

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Last updated on August 5, 2025

The numbers that have only two factors, which are 1 and itself, are called prime numbers. For encryption, computer algorithms, barcode generation, prime numbers are used. In this topic, we will be discussing whether 1387 is a prime number or not.

Is 1387 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 1387 has more than two factors, it is not a prime number.

Why is 1387 Not a Prime Number?

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1387 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

  • Counting Divisors Method
     
  • Divisibility Test
     
  • Prime Number Chart
     
  • Prime Factorization

Using the Counting Divisors Method

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 1387 is prime or composite.

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

Step 2: Divide 1387 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 1387 by 3. The sum of its digits (1 + 3 + 8 + 7 = 19) is not divisible by 3.

Step 4: Divide 1387 by 11. The difference between the sum of its digits in odd positions (1 + 8) and even positions (3 + 7) is 1, which is not divisible by 11.

Step 5: Continue checking divisibility up to approximately the square root of 1387. Since 1387 is divisible by 19 (1387 ÷ 19 = 73), it has more than 2 divisors, making it a composite number.

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Using the Divisibility Test Method

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: 1387 is not divisible by 2, as it is an odd number.

Divisibility by 3: The sum of the digits in 1387 is 19, which is not divisible by 3.

Divisibility by 5: The unit's place is not 0 or 5; hence, it is not divisible by 5.

Divisibility by 7: By performing the divisibility rule for 7, 1387 is not divisible by 7.

Divisibility by 11: 1387 is not divisible by 11, as explained previously. Since 1387 is divisible by 19, it has more than two factors. Therefore, it is a composite number.

Using Prime Number Chart

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 a numerical table.

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 for other primes. Through this process, we will have a list of prime numbers. Since 1387 is not in the list, it confirms that it is a composite number.

Using the Prime Factorization Method

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 1387 as 19 × 73.

Step 2: Both 19 and 73 are prime numbers, making this the prime factorization of 1387.

Common Mistakes to Avoid When Determining if 1387 is Not a Prime Number

Children might have some misconceptions about prime numbers when they are learning about them. Here are some mistakes that might be made by children.

FAQ on is 1387 a Prime Number?

1.Is 1387 a perfect square?

2.What is the sum of the divisors of 1387?

The sum of the divisors of 1387, including 1, 19, 73, and 1387, is 1480.

3.What are the factors of 1387?

1387 is divisible by 1, 19, 73, and 1387, making these numbers the factors.

4.What are the closest prime numbers to 1387?

1381 and 1389 are the closest prime numbers to 1387.

5.What is the prime factorization of 1387?

The prime factorization of 1387 is 19 × 73.

Important Glossaries for "Is 1387 a Prime Number"

  • Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1387 is a composite number because it is divisible by 1, 19, 73, and 1387.
     
  • Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1387 is 19 × 73.
     
  • Divisibility test: A set of rules to determine whether one number is divisible by another without performing division.
     
  • Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.
     
  • Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 4 and 9 are co-prime.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.