Is 1601 a prime number?

The number 1601 has 2 factors, which are 1 and 1601 itself. Thus, the number 1601 is a prime number. Since it does not have any other divisors, it is categorized as a prime.

A number to be a prime number should follow the criteria that it should not have factors more than 2. Here, 1601 has only 2 factors, 1 and 1601, hence making it a prime number.

Given below are a few ways that can be used to check if a number is prime or composite.

The different methods we can use to check if a number is a prime number are explained below:

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

For the counting divisors method, it is checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 1601 would simply be:

Divisors of 1601 = 1, 1601
Number of divisors = 2

Since the number 1601 has only 2 divisors, it is considered a prime number.

In the divisibility test, we try to divide the number by any of the prime numbers. If it is not divisible by any, then it is considered a prime number.

In the divisibility method, the prime number only has 2 divisors, which are 1 and itself.

The divisors of 1601 are 1 and 1601.

Thus, 1601 consists of only 2 factors, making it a prime number.

The prime number chart is a list of prime numbers starting from 2 to infinity.

The list of prime numbers from 1500 to 1700 are:
1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699

1601 is in this list, therefore 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, 1601 is a prime number because its only divisors are 1 and 1601.

Divisibility Test: A method used to check if one number is divisible by another without performing division. For example, using this test on 1601, we check if it is divisible by smaller prime numbers like 2, 3, 5, etc.

Counting Divisors Method: A technique to check how many divisors a number has. A prime number has exactly two divisors: 1 and the number itself. In the case of 1601, its divisors are 1 and 1601.

Composite Number: A number that has more than two divisors. It is the opposite of a prime number. 1601 is not composite because it only has two divisors.

Prime Factorization: The process of expressing a number as a product of its prime factors. Since 1601 is prime, its prime factorization is simply 1601 itself.