Is 626 a Prime Number?

Numbers can be categorized as either prime numbers or composite numbers based on the number of factors they have.

A prime number is a natural number greater than 1 that is divisible only by 1 and itself. For example, 5 is a prime number because it is divisible by 1 and 5.

A composite number is a positive number that is divisible by more than two numbers. For example, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Prime numbers have several properties:

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

Since 626 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 626 has more than two factors, it is not a prime number. There are several methods used to determine whether a number is prime or composite:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization

The counting divisors method involves counting the number of divisors a number has to determine whether it is prime or composite. If a number has exactly 2 divisors, it is prime. If it has more than 2, it is composite. Let’s check whether 626 is prime or composite:

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

Step 2: Divide 626 by 2. It is divisible by 2, so 2 is a factor of 626.

Step 3: Check divisibility by numbers up to the square root of 626.

Since 626 is divisible by numbers other than 1 and itself, it is a composite number.

The Divisibility Test Method uses a set of rules to determine whether a number is divisible by another number without leaving a remainder.

Divisibility by 2: 626 ends in 6, an even digit, so it is divisible by 2.

Divisibility by 3: The sum of the digits (6 + 2 + 6 = 14) is not divisible by 3.

Divisibility by 5: 626 does not end in 0 or 5, so it is not divisible by 5.

Divisibility by 11: Alternating sum of digits (6 - 2 + 6 = 10) is not divisible by 11. Since 626 is divisible by 2, it has more than two factors, making it a composite number.

A prime number chart, often generated using the Sieve of Eratosthenes, can help identify prime numbers. The steps involved are:

Step 1: Write numbers from 1 to 100 in a grid.

Step 2: Leave 1 unmarked as it is neither prime nor composite.

Step 3: Mark 2 as prime and cross out its multiples.

Step 4: Mark 3 as prime and cross out its multiples.

Step 5: Continue this process until all numbers are checked. In the range of numbers up to 100, 626 does not appear as a prime number, confirming it is composite.

Prime factorization involves breaking down a number into its prime factors:

Step 1: Divide 626 by 2 to get 313.

Step 2: Check if 313 is prime by attempting to divide by prime numbers up to its square root.

Step 3: Since 313 is not divisible by any primes below its square root, it is a prime number. Thus, the prime factorization of 626 is 2 × 313.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 626 is a composite number because it is divisible by 1, 2, 313, and 626.

• Prime factorization: The process of expressing a number as the product of its prime factors, such as 626 = 2 × 313.

• Divisibility rules: Guidelines to determine if one number is divisible by another without performing the division.

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

• Co-prime numbers: Two numbers that have only 1 as their greatest common divisor. For example, 14 and 15 are co-prime.