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How Many Factors Does a Prime Number Have

How Many Factors Does a Prime Number Have

Edited By Team Careers360 | Updated on Jun 07, 2023 10:27 AM IST

Introduction

The number of the factors of a prime number is two only. How do we get it? To arrive at the answer to this question, first, we have to understand what a prime number is and what the “multiples” and “factors” of a number are. As such, you are aware of the multiplication tables. Each multiplication table is, essentially, a tabular illustration involving factors and multiples of numbers. Among these multiples and factors of different numbers, you may discover certain common factors and common multiples. Sometimes the numbers will show no common factor except 1. Isn’t it right? Let us explore the concepts of factors in detail.

What is a Factor?

Suppose we inspect a multiplication table in which we get that the number P equals the product of another number p and the number q. The mathematical expression is the following.

P=p×q

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Now we divide the number P by p, or q, to find that P is completely divisible by p and q.

P÷p=qA÷q=p

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So, we realize that both p and q are the factors of the number P.

Thus, we see that if an integer divides any number entirely leaving no remainder, we conclude that the integer is the factor of that number.

What is Multiple?

Let us observe another multiplication statement where the number Q is equal to the product of the numbers q and r which is expressed as the following.

Q=q×r

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Here, we can interpret that by multiplying the number q with another number r, we get the number Q which is greater than both q and r.

So, we achieve that the number Q is the multiple of both the numbers q and r.

Thus, we catch that if an integer is multiplied by another integer, we deduce that the resultant product that is also an integer is, actually, the multiple of both the first and the second integers.

What is a Prime Number?

When we factorize any number and we get that the number has only two factors (1, and the number itself), we refer to it as a prime number.

Examples of prime numbers are 2, 3, 5, 7, etc.

The prime number is a factor to itself

What is a Composite Number?

Note that when the factorization of any number results in more than two factors of the number, we get a composite number.

Examples of composite numbers are 4,6,9, etc.

The Factors of a Prime Number

To find the factors of a prime number we can factorize it. But we will not get more than two factors of a prime number.

It is evident that the only possible multiplication to obtain the resulting product as the prime number itself is only one.

Thus, any prime number has only two factors.

Interpretation of The Multiplication Operation

We see that multiplication provides us with the product of numbers. So, we can represent the multiplication operation with the following interpretation.

  • Both the multiplicands and the multipliers in the calculation of multiplication indicate the factors.

  • The product gained from the process of multiplication is, obviously, a multiple.

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Conclusion

  • The number one is neither a prime nor a composite number.

  • Every factor of any number when dividing the concerned number yields no remainder in the division.

  • On multiplying any number of factors we obtain the multiple.

  • From the factors of any given set of numbers, we can find out their highest common factor.

  • From the multiples of any given set of numbers, we can find out their least common factor.

  • The prime number is its own factor.

  • The prime number is its own multiple.

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