Is 967 a prime number?

The number 967 has only 2 factors, which are 1 and 967 itself. Thus, 967 is a prime number.

A number is considered a prime number if it has no factors other than 1 and the number itself. Since 967 only has these two factors, it qualifies as a prime 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, we check whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 967 would simply be: Divisors of 967 = 1, 967

Number of divisors = 2

Since the number 967 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 we cannot divide the number by any prime numbers other than 1 and the number itself, then it is considered a prime number.

For 967, no prime number divides it exactly, so it is a prime number.

The prime number chart is the list of prime numbers starting from 2 to infinity. The list of prime numbers under 1000 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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.

Since 967 is present in the list, it is confirmed as a prime number.

Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 967 is a prime number because it has only 1 and 967 as its divisors.

Divisors: The numbers that divide evenly into a given number. For example, the divisors of 967 are 1 and 967.

Divisibility Test: A method used to check if a number is divisible by another without actually performing the division. It involves checking for divisibility by prime numbers.

Composite Number: A natural number greater than 1 that has more than two distinct divisors. Since 967 only has two divisors (1 and 967), it is not a composite number.

Prime Factorization: The process of expressing a number as the product of prime numbers. Since 967 is prime, its prime factorization is simply 967 itself.