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
Answers
Answered by
128
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.
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.
Answered by
32
Answer:
in which of the following expressions prime factorisation has been done?
Similar questions