Prime Factorisation of 20570, 58500 and 45470971

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Determine the prime factorisation of each of the following positive integers:

(i) 20570    (ii) 58500    (iii) 45470971

(i) Prime Factorisation of 20570

20570 = 2 × 10285
= 2 × 5 × 2057
= 2 × 5 × 11 × 11 × 17

∴ 20570 = 2 × 5 × 11² × 17

(ii) Prime Factorisation of 58500

58500 = 585 × 100
= (3 × 3 × 5 × 13) × (2 × 2 × 5 × 5)

∴ 58500 = 2² × 3² × 5³ × 13

(iii) Prime Factorisation of 45470971

45470971 = 17 × 2674763
2674763 = 19 × 140777
140777 = 7 × 20111

∴ 45470971 = 7 × 17 × 19 × 20111

(20111 is a prime number)

Final Answer

20570 = 2 × 5 × 11² × 17
58500 = 2² × 3² × 5³ × 13
45470971 = 7 × 17 × 19 × 20111

Conclusion

Thus, each of the given integers has been expressed as a product of its prime factors using the method of prime factorisation.