Question

Question 9 In which of the following expressions, prime factorization has been done? (a) 24 = 2 × 3 × 4 (b) 56 = 7 × 2 × 2 × 2 (c) 70 = 2 × 5 × 7 (d) 54 = 2 × 3 × 9

Class 6 - Math - Playing with Numbers Page 62

Answer 1

First recall that prime numbers are the numbers that have only two factors, 1 and itself. For example, 3 is a prime number which only have the factors 1 and 3, i.e., 1 and the number itself. 
Now, I am going to solve your questions. 
a) 24 = 2 × 3 × 4
In prime factorization, we only write a number as the product of its prime numbers. In this method, we don't write composite numbers. 
See that in this factorization, 24 is written as the product of 2, 3 and 4. 2 and 3 are prime numbers, but 4 is a composite number. In prime factorization, we don't write composite numbers. All the factors should be prime numbers in this method. As we know that 4 is a composite number. 
∴ This is not prime factorization. 

b) 56 = 7 × 2 × 2 × 2
In this factorization, all the factors of 56 are prime numbers. There is no composite number. 
∴ This is prime factorization. 

c) 70 = 2 × 5 × 7
In this factorization, all the factors of 70 are prime numbers. There is not composite number in this process of factorization. 
∴ This is prime factorization. 

d) 54 = 2 × 3 × 9
In this factorization, 54 is written as the product of 2, 3 and 9. In this factorization, 2 and 3 are prime numbers, but 9 is a composite number. 
∴ This is not prime factorization. 

Hope this may help you. 

Answer 2

Answer:

in which of the following expressions prime factorisation has been done?