Is 400 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 400 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 400 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

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 400 is prime or composite.

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

Step 2: Divide 400 by 2. It is divisible by 2, so 2 is a factor of 400.

Step 3: Divide 400 by 4. It is divisible by 4, so 4 is a factor of 400.

Step 4: You can simplify checking divisors up to 400 by finding the root value, which is 20. We then need to only check divisors up to the root value.

Step 5: When we divide 400 by 2, 4, 5, 8, 10, 16, and 20, it is divisible by all these numbers. Since 400 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 0. Zero is an even number, which means that 400 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 400 is 4. Since 4 is not divisible by 3, 400 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 0. Therefore, 400 is divisible by 5.

Divisibility by 10: The unit’s place digit is 0. Therefore, 400 is divisible by 10. Since 400 is divisible by 2, 4, 5, and 10, 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 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, 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. 400 is not present in the list of prime numbers, so 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 400 as 2×200.

Step 2: In 2×200, 200 is a composite number. Further, break 200 into 2×100.

Step 3: Continue breaking down 100 into 2×50, and then 50 into 2×25, and finally 25 into 5×5.

Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 400 is 2×2×2×2×5×5.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 400 is a composite number because it is divisible by 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 400 include 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.

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

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