Is 945 a prime number?

The number 945 has got multiple factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 945 is a non-prime number. The factors of 945 include 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945.

A number to be a prime number should follow the criteria that it should not have factors more than 2. Here, 945 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 945 would simply be

Divisors of 945 = 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
Number of divisors = 16

The number 945 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 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945.

Thus, 945 consists of 16 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 under 100 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

945 is not present in the list, it is not a prime number.

This method is only used for a non-prime number/composite number. Since 945 is a composite number, the prime factorization for 945 is:

Factors of 945 = 3 × 3 × 3 × 5 × 7

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 distinct positive divisors. For example, 4, 6, and 945 are composite numbers.

Divisors: Numbers that divide another number completely without leaving a remainder. For example, the divisors of 945 are 1, 3, 5, 7, 9, and so on.

Prime Factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 945 is 3×3×3×5×7​​​​​​.

Divisibility Rule: A set of guidelines to quickly determine if a number is divisible by another without performing long division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.