In Which of the following Expressions Prime Factorization has been Done:


Question: 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

Prime factorization is a way of expressing a number as a product of its prime factors

Answer: Prime factorization has been done for (b) 56 = 7 × 2 × 2 × 2   (c) 70 = 2 × 5 × 7

For the product to be represented in terms of it's prime factors, the factors should be prime numbers

Explanation:

(a) 24 = 2 × 3 × 4:  4 is not a prime number, hence 24 is not expressed as it's product of prime factors

(b) 56 = 7 × 2 × 2 × 2: 7 and 2 are prime numbers. So, 56 is expressed as the product of prime factors

(c) 70 = 2 × 5 × 7: 2, 5, and 7 are prime numbers. So, 70 is expressed as the product of prime factors

(d) 54 = 2 × 3 × 9 : 9 is not a prime number, hence 54 is not expressed as it's product of prime factors

Thus, prime factorization has been done for (b) 56 = 7 × 2 × 2 × 2   (c) 70 = 2 × 5 × 7