Question

Give the prime factorization of the number $48$.

Answer 1

Hint: Prime factorization is a process of factoring a number in terms of prime numbers i.e., the factors will be prime numbers. Here, we have to start by dividing the given number by the first prime number \[2\] (as $48$ is an even number) and continue dividing by \[2\] until you get a decimal or remainder. Then divide by \[3,5,7\], etc. until the only numbers left are prime numbers. Then write the given number as a product of prime numbers.

Complete step by step solution:
A prime number is a counting number if it has exactly two factors, namely itself and \[1\]. Examples are \[2,3,5,7,9,11,13,....\] etc. Factors are numbers that can be multiplied together to make another number. So, prime factorization is writing the prime numbers that will multiply together to make a new number as a multiplication problem.

Given number is \[48\]. Since \[48\] is divided by \[2\] and gives \[24\] i.e., \[\dfrac{{48}}{2} = 24\]. Divide the number \[24\] by \[2\] and give \[12\] i.e., \[\dfrac{{24}}{2} = 12\]. Divide the number \[12\] by \[2\] and give \[6\] i.e., \[\dfrac{{12}}{2} = 6\]. Divide the number \[6\] by \[2\] and give \[3\] i.e., \[\dfrac{6}{2} = 3\]. Since \[3\] is a prime number.

Hence, the prime factorization of the number \[48\] is \[48 = {2^4} \times 3\].

Note:
Co-primes are two numbers whose H.C.F is \[1\]. Examples are \[\left( {4,5} \right)\],\[\left( {3,5} \right)\],\[\left( {4,9} \right)\],…etc. Co-primes are also called relative primes. Twin primes are two prime numbers whose difference between two examples are \[\left( {3,5} \right)\], \[\left( {5,7} \right)\], … etc. Since two primes must be odd to become twin primes.