Page 179 - Demo

178 Arrow-Puffin-4_Semester-1 MathsWhen a number is expressed as a product of prime numbers, we call it prime factorization. A factorization in which every factor is prime, is called the prime factorization of the number.Prime factorization of 30 and 48 are given below : 30 = 2 x 3 x 5 48 = 2 x 2 x 2 x 2 x 3This can be done in two ways : Division method and Factor tree method.Prime Fractorization using Division MethodTo make the prime factorization of a number, we divide the given number by the prime numbers 2, 3, 5, 7 and 11 etc., in this order repeatedly so long as the quotient is divisible by that number.Example 1 : Express 72 as the product of prime numbers.Solution : 2 72 Dividing by 22 36 Dividing by 22 18 Dividing by 23 9 Dividing by 33 3 Dividing by 31 Hence, 72 = 2 x 2 x 2 x 3 x 3.Prime Fractorization using Factor Tree MethodIn this method, we factorize the composite number till we get all its prime numbers.We obtain all the prime factors by drawing a diagram, known as a factor tree.Examples : Draw a factor tree to show the prime factorization of 42 and 80.Solution : 80 2 x 40 2 2 x 20 2 2 2 x 10 2 2 2 2 x 5 42 2 x 21 2 3 x 7Example 2 : Express 125 as the product of prime numbers.Solution : 5 125 Dividing by 55 25 Dividing by 55 5 Dividing by 51Hence, 125 = 5 x 5 x 5.