Is 1613 a prime number?

A number is considered a prime number if it has only 2 factors: 1 and the number itself. Since 1613 meets this criterion, it is a prime number.

Below are some commonly used methods to verify if a number is prime or composite.

Methods to check if a number is a prime number:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization

In this method, we count the total divisors of the number.

For 1613:

Divisors of 1613 = 1, 1613
Number of divisors = 2

Since 1613 has only 2 divisors, it is a prime number.

Here, the number is tested for divisibility by smaller prime numbers (like 2, 3, 5, 7, etc.).

1613 is not divisible by any smaller prime number, confirming it has no divisors other than 1 and itself.
Thus, 1613 qualifies as a prime number.

A prime number chart lists all prime numbers starting from 2 onward.

The list of prime numbers from 1600 to 1700 are:
1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699

Since 1613 is present in this list, it is a prime number.

Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 1613 is a prime number.

Divisors: Numbers that divide another number completely without leaving a remainder. For instance, the divisors of 1613 are 1 and 1613.

Composite Number: A natural number greater than 1 that has more than two distinct positive divisors. For example, 12 is a composite number because it has divisors 1, 2, 3, 4, 6, and 12.

Prime Factorization: Expressing a number as a product of its prime factors. For a prime number like 1613, the factorization is simply 1613 × 1.

Divisibility Test: A method to determine if one number can divide another number without leaving a remainder.