Finding the factors of a small number is an elementary concept in Mathematics. For finding a number of factors of larger numbers, we have a factor theorem and some other techniques. In this article, we are going to find the factors of 23 and what makes 23 a prime number. Consider a number N. Then N's factors will be those numbers that will divide N leaving the remainder zero. Similarly, factors of 23 will be those numbers which will divide 23 leaving the remainder zero. All the numbers have 1 and the number itself as the two factors. As 1 × N = N.
When we divide N by 1 or by N we will always get remainder zero. We can say there are at least two factors of a given number. Fraction numbers or decimal numbers are not considered as factors.
In this method, we will continuously divide the given number by its prime factors. Let's say we are given number 16. Then by prime factorization method, we get
16 = 2 × 2 × 2 × 2.
To find negative factors, simply assign the -ve sign behind the numbers.
From the above intuition, we get factors of 23 are 1 and 23. So it's negative factors come out to be -1 and -23.
The number of factors of a given number let's say 8 ( by factor theorem)?
Step 1 — from prime factorization method we can get 8 = 2 × 2 × 2
Step 2 — write the prime factors in exponential al form — 2^3
Step 3 — leaving the base we consider the number in the exponent.
3 +1 = 4 hence 8 has 4 factors.
In case of our number 23 = 1 × 23
It is a prime number hence the factor theorem has a different approach to prime numbers.
The number of positive factors of a prime number is always 2. The factor theorem has this special case for prime numbers.
1 is always a factor of every number
The number itself is the largest factor of that number
e.g - The largest factor of 23 is 23.
Every factor of a number is the exact divisor of that number.
For every number, there are only finite factors for that.
We can conclude that 23 is a prime number as it has only two factors: the number 1 and the number itself. There are many other ways to prove a number is prime by using a primality test but it is beyond the scope of this article. We got how the number 23 has only two factors and hence it is a prime number.
1. Is 1 Itself a Prime Number?
No, 1 is not a prime number as it does not satisfy the definition of a prime number. The definition of prime number states that any number is called prime if there are only two factors of it i.e. the number itself and 1. But ambiguity in this condition is that both the numbers must be different from each other. In the case of 1, both the numbers are coming to the same hence, 1 is not a prime number.
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