The factors of the greatest two-digit prime number are 1 and 97.
The Greatest Two-Digit Prime Number
To determine the factors, we first need to identify the greatest two-digit prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. When examining two-digit numbers, we look for those that fit this definition. While numbers like 2, 3, 5, and 7 are prime, they are single-digit numbers and are therefore not considered in this context.
Through the process of elimination and testing for divisibility, it is found that 97 is the largest prime number consisting of two digits. All prime numbers, by definition, possess a unique characteristic: they have only two factors.
Understanding Factors of a Prime Number
A factor of a number is an integer that divides the number evenly, leaving no remainder. For any prime number, this definition simplifies greatly.
Every prime number, by its very nature, adheres to a specific factorization rule:
- It is always divisible by 1.
- It is always divisible by itself.
No other whole number can divide a prime number evenly without leaving a remainder.
Factors of 97
Since 97 is a prime number, its factors are precisely 1 and 97. There are no other integers that can divide 97 without leaving a remainder.
Here's a simple representation of its factors:
| Number | Factors |
|---|---|
| 97 | 1, 97 |
This property is fundamental to the definition of prime numbers, making their factorization straightforward and unique.
