Is 1407 a Prime Number?
2026-02-28 13:38 Diff
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Last updated on February 3, 2026

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 1407 is a prime number or not.

Is 1407 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 that is 1.
     
  • As 1407 has more than two factors, it is not a prime number.

Why is 1407 Not a Prime Number?

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1407 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. A few methods are:

  • 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 1407 is prime or composite.

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

Step 2: Divide 1407 by 2. It is not divisible by 2 as it is odd.

Step 3: Divide 1407 by 3. The sum of the digits is 12, which is divisible by 3. So, 3 is a factor of 1407.

Since 1407 has more than 2 divisors, it is 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: 1407 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1407 is 12. Since 12 is divisible by 3, 1407 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1407 is not divisible by 5.

Divisibility by 7: Double the last digit (7 × 2 = 14) and subtract it from the rest of the number (140 - 14 = 126). Since 126 is divisible by 7, 1407 is also divisible by 7.

Since 1407 is divisible by 3 and 7, 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 sequence.

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 a table consisting of marked and crossed boxes, except 1.

1407 is not present in the list of prime numbers, so it is a composite number.

Using the Prime Factorization Method

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 1407 as 3 × 469.

Step 2: In 3 × 469, 469 is a composite number. Further, break 469 into 7 × 67.

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

Hence, the prime factorization of 1407 is 3 × 7 × 67.

Common Mistakes to Avoid When Determining if 1407 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 1407 a Prime Number?

1.Is 1407 a perfect square?

2.What is the sum of the divisors of 1407?

The sum of the divisors of 1407 is not straightforward to calculate without a complete list of divisors.

3.What are the factors of 1407?

1407 is divisible by 1, 3, 7, 21, 67, 201, 469, and 1407, making these numbers the factors.

4.What are the closest prime numbers to 1407?

1409 and 1409 are the closest prime numbers to 1407.

5.What is the prime factorization of 1407?

The prime factorization of 1407 is 3 × 7 × 67.

Important Glossaries for "Is 1407 a Prime Number"

  • Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
  • Prime numbers: Natural numbers greater than 1 that are divisible by only 1 and itself. For example, 5 is a prime number because it is divisible only by 1 and 5.
  • Divisibility rules: Guidelines to determine if a number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.
  • Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 18 is 2 × 3 × 3.
  • Co-prime numbers: Two numbers with only one common factor, which is 1. For example, 8 and 15 are co-prime numbers.

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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.