Is 1478 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 1478 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 1478 has more than two factors, it is not a prime number. Here are a few methods used to distinguish between prime and composite numbers:

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 1478 is prime or composite.

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

Step 2: Divide 1478 by 2. It is divisible by 2, so 2 is a factor of 1478.

Step 3: Divide 1478 by 3. It is not divisible by 3, so 3 is not a factor of 1478.

Step 4: You can simplify checking divisors up to 1478 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1478 by 2 and 739, it is divisible by both.

Since 1478 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 8. Since 8 is an even number, 1478 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1478 is 20. Since 20 is not divisible by 3, 1478 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 1478 is not divisible by 5.

Divisibility by 7: The last digit in 1478 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (147 - 16 = 131). Since 131 is not divisible by 7, 1478 is also not divisible by 7.

Divisibility by 11: In 1478, the difference between the sum of the digits in odd positions (1 + 7 = 8) and the sum of the digits in even positions (4 + 8 = 12) is 4. This would mean that 1478 is not divisible by 11.

Since 1478 is divisible by 2 and 739, 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 from 1 to 100 in 10 rows and 10 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, we will have a list of prime numbers from 1 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 1478 is greater than 100, we cannot conclude directly from this chart, but as it is divisible by 2, it is not a prime 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 1478 as 2 × 739.

Step 2: 739 is a composite number, so we stop here as 739 cannot be further simplified into smaller prime factors.

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

Hence, the prime factorization of 1478 is 2 × 739.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1478 is a composite number because it is divisible by 1, 2, 739, and 1478.

• Prime numbers: Natural numbers greater than 1 that have exactly two distinct positive divisors: 1 and themselves.

• Divisibility rules: A set of rules that help determine whether a number is divisible by another without performing division.

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

• Divisors: Numbers that divide another number exactly without leaving a remainder. For example, the divisors of 4 are 1, 2, and 4 because they divide 4 completely.