How Many Factors in Composite Numbers

Introduction

Numbers with more than two factors are referred to as composite numbers in mathematics. The antithesis of prime numbers, which only contain two factors—the number itself and the number one—are composite numbers. Zero (0) is not regarded as either a prime number or a composite number since it has no factors. All natural numbers that are not prime numbers are considered composite numbers because they can be divided by more than two numbers.

Explantion

Based on factorization, numbers can be divided into two categories:

• Prime numbers: A prime number only has two elements, namely one and the number itself.

• Composite numbers: A composite number is composed of multiple variables.

How to Find Factors of Composite Numbers

• The given number whose factors are to be determined is divided by the smallest prime.

• Divide by that prime again and again until it stops dividing evenly.

• Divide by the following prime until the division is no longer equal. Until the quotient is prime, keep going.

• The sum of all the primes at the bottom, sides, and top of the ladder is the composite number.

Demonstration

Let us find the factors of the number 150. We will first divide 150 by the smallest prime number that will give the remainder zero. In this case, it's two.

\mathrm{\frac{150}{2}}=\mathrm{75}

\mathrm{\frac{75}{3}}=\mathrm{25}

\mathrm{\frac{25}{5}}=\mathrm{5}

\mathrm{\frac{5}{5}}=\mathrm{1}

Here we can say that the factors of 150 are 2,3 and 5 . Since it has more than two factors 150 is a composite number.

How to Find Total Number of Factors of a Composite Number

1. Find the prime factorization of the given number.

2. Now let us have a number N which has prime factors a, b, c and so on which are repeated a times, b times, c times and so on. And, the prime factorisation of the number N is given by N=ap.bq.cr….

3. Now, the total number of factors are given by (p+1)(q+1)(r+1).... - 1

Conclusion

In conclusion, we can say that a composite number will have more than two factors for sure. The exact number of factors varies from number to number which can be given by the formula we have discussed.