A number system is a method of showing numbers by writing, which is a mathematical way of representing the numbers of a given set, by using the numbers or symbols in a mathematical manner. The writing system for denoting numbers using digits or symbols in a logical manner is defined as a number system, which Represents a useful set of numbers also Reflects the arithmetic and algebraic structure of a number, and Provides standard representation. Show Prime FactorizationIt is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers. Here are some of the prime factorization concepts, First, the simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 70 we get, 70/2 =35 , 35/5 = 7, 7/7 = 1. Since we received the remainder, it cannot be further factorized. Therefore, 70 = 2 x 5 x 7, where 2, 5 and 7 are prime factors. There are few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and so on. These prime numbers when multiplied with any of the natural numbers produce composite numbers. Prime Factorization Method Prime factorization is a way of showing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. It is also defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors. As we all know, a composite number has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers. For example, here the prime factors of 126 will be 2, 3, and 7 as 2 × 3 × 3 × 7 = 126, and 2, 3, 7 are prime numbers. An example of the number 40 is 5 × 8, but 8 is not a prime number. The number 8 is expressed as 2 ×2 × 2 since 5 and 2 are prime numbers. Therefore, the prime factorization of 40 is 2 × 2 × 2 × 5 = 23 × 5. Some of the commonly used prime factorization methods Division MethodSteps to calculate the prime factors of a number is similar to the process of finding the factors of a large number. Follow the below steps to find the prime factors of a number using the division method: Some of the steps are
Question: Do the prime factorization of 460. Solution:
Factor Tree MethodIn this method, the factors of a number are found and then those numbers are further factorized until we reach the prime numbers. For the evaluation of the prime factorization of a number using the factor tree method, here are the steps given below:
Question: What is the prime factorization of 70 and 300 using the Factor tree method? Solution:
What is the least number by which 8640 is divided, the quotient as a complete cube number?Solution:
Question 1: Find the least number by which 7803 is divided, the quotient as a complete cube number? Solution:
Question 2: What is the least number by which 107811 is divided, the quotient as a complete cube number? Solution:
With what least number must 8640 be divided so that the quotient is a perfect cube? The prime factors of 8640 are
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5= (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x 5 Clearly, 8640 must be divided by 5. Concept: Cube Root Through Prime Factorisation Method Is there an error in this question or solution? |