Is 1461 a prime number?

The number 1461 has 4 factors, that are capable of dividing the number completely without leaving any remainder. Thus the number 1461 is a non-prime number. The factors of 1461 include 1, 3, 487, and 1461.

 A number to be a prime number should follow the criteria, which is that it should not have factors more than 2.

Here, 1461 has more than 2 factors, hence making it a composite number. Given below are a few ways that can be used to find prime or composite numbers.

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 to be checked whether the number is divisible by any numbers other than 1 and the number itself. The counting divisors method for 1461 would simply be: Divisors of 1461 = 1, 3, 487, 1461 Number of divisors = 4 The number 1461 can be considered composite.

In the division test, we try to divide the number by any of the prime numbers. If we cannot, 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 1461 are 1, 3, 487, and 1461. Thus, 1461 consists of 4 factors that divide it completely without any remainder.

The prime number chart is the list of prime numbers starting from 2 to infinity. The list of prime numbers from 1400 to 1500 includes: 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499. 1461 is not present in the list, so it is not a prime number.

This method is only used for a non-prime number/composite number. Since 1461 is a composite number, the prime factorization for 1461 is: Factors of 1461 = 3 × 487

Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers.

Composite Number: A natural number greater than 1 that has more than two divisors. These numbers can be divided evenly by numbers other than 1 and itself. For example, 4, 6, and 1461 are composite numbers.

Divisors: The numbers that divide another number completely without leaving a remainder. For 1461, the divisors are 1, 3, 487, and 1461.

Prime Factorization: The expression of a composite number as the product of prime numbers. For 1461, the prime factorization is 3 × 487.

Divisibility Test: A method used to determine whether one number can be divided by another without leaving a remainder. If a number can be divided evenly by a prime number, it is not prime.