Question

Express 16380 as product of its prime factors. The factorisation is unique, why?​

Answer 1

Answer:

The orange divisor(s) above are the prime factors of the number 16,380. If we put all of it together we have the factors 2 x 2 x 3 x 3 x 5 x 7 x 13 = 16,380. It can also be written in exponential form as 22 x 32 x 51 x 71 x 131.26-Apr-2018

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given :-

16380

To find :-

Express 16380 as product of its prime factors. The factorisation is unique, why?

Solution :-

See the above attachment

Given number = 16380

16380 = 2×2×3×3×5×7×13

or

16380 = 3×3×5×7×13×2×2

or

16380 = 5×7×13×2×2×3×3

or

16380 = 7×13×2×2×3×3×5×5

We write like this so many types

We get the prime factors 2,3,5,7,13

So, 16380 = 2²×3²×5¹×7¹×13¹

The above patterns are different but the prime factors are same .

This is called Fundamental Theorem of Arithmetic.

Fundamental Theorem of Arithmetic:-

"Every composite number can be expressed as the product of primes and this prime factorization is unique apart from the order in which the prime factors occur" .

Answer :-

16380 = 2×2×3×3×5×7×13 or 2²×3²×5¹×7¹×13¹

This prime factorization is unique.

Used formulae:-

Fundamental Theorem of Arithmetic:-

"Every composite number can be expressed as the product of primes and this prime factorization is unique apart from the order in which the prime factors occur" .