Is 990 a Prime Number?

Numbers can be categorized as prime or composite based on the number of their 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 only 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 have the following properties:

Prime numbers are positive numbers greater than

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 because they have only one common factor, which is 1.

Since 990 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is having only two divisors: 1 and itself. Since 990 has more than two factors, it is not a prime number. Several methods can distinguish between prime and composite numbers, including:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The counting divisors method categorizes numbers as prime or composite by counting their divisors. A number with exactly two divisors is prime, while a number with more than two divisors is composite. Let's apply this to 990:

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

Step 2: Divide 990 by 2. It is divisible by 2, so 2 is a factor of 990.

Step 3: Divide 990 by 3. It is divisible by 3, so 3 is a factor of 990.

Step 4: Continue dividing by numbers up to the square root of 990.

Step 5: 990 is divisible by several numbers, including 2, 3, 5, and more. Since 990 has more than 2 divisors, it is a composite number.

The divisibility test method uses a set of rules to check whether a number is divisible by another number completely.

Divisibility by 2: The last digit of 990 is 0. Since 0 is even, 990 is divisible by 2.

Divisibility by 3: The sum of the digits in 990 is 18 (9+9+0), which is divisible by 3, so 990 is also divisible by 3.

Divisibility by 5: The last digit is 0, so 990 is divisible by 5.

Divisibility by 7: When using the divisibility rule for 7, 990 is divisible by 7.

Divisibility by 11: The alternating sum of the digits is 0, which is divisible by 11, so 990 is also divisible by 11. Since 990 is divisible by multiple numbers, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” This method involves:

Step 1: Writing numbers from 1 to 100 in 10 rows and 10 columns.

Step 2: Leaving 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Marking 2 as a prime number and crossing out all multiples of 2.

Step 4: Marking 3 as a prime number and crossing out all multiples of 3.

Step 5: Repeating this process until you reach a table consisting of marked and crossed boxes, except 1. The resulting list contains all prime numbers from 1 to 100. Since 990 is not on the list of prime numbers, it is a composite number.

Prime factorization involves breaking down a number into its prime factors and multiplying them to obtain the original number.

Step 1: We can write 990 as 2 × 495.

Step 2: Break down 495 into 3 × 165.

Step 3: Break down 165 into 5 × 33.

Step 4: Break down 33 into 3 × 11. Thus, the prime factorization of 990 is 2 × 3 × 3 × 5 × 11.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.

• Prime numbers: Natural numbers greater than 1 with exactly two distinct positive divisors: 1 and the number itself.

• Divisibility: The ability for one number to be divided by another without leaving a remainder.

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

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