Question

. Express each of the following integers as a product of its prime factors:
(i) 420
(ii) 468
(iii) 945
(iv) 7325
of each of the following positive integer


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Answer 1

Answer:

According to the fundamental theorem of arithmetic , every composite number can be written as the product of primes and this factorization is unique.

**Composite number = Product of prime numbers

**Any integer greater than one, either be a prime number or can be written as a product of prime factors.

(i) Given number =  420

420 = 2 x 2 x 3 x 5 x 7 = 2² × 3¹ × 5¹ × 7¹

Hence, 420 can be expressed as a product of its prime factor which is 2² × 3¹ × 5¹ × 7¹.

 

(ii) Given number = 468

468 = 2 x 2 x 3 x 3 x 13 = 2² × 3² × 13¹

Hence, 468 can be expressed as a product of its prime factor which is 2² × 3² × 13¹.

 

(iii) Given number = 945

945 = 3 x 3 x 3 x 5 x 7 = 3³ × 5¹ × 7¹

Hence, 945 can be expressed as a product of its prime factor which is 3³ × 5¹ × 7¹.

(iv) Given number = 7325

7325 = 5 x 5 x 293 = 5² × 293

Hence, 7325 can be expressed as a product of its prime factor which is 5² × 293.

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