Question

The number of ways in which \( N=2,778,300 \) can be resolved into the two factors prime to each other. 

(1) 10 

(2) 9 

(3) 8 

(4) 7

Answer 1

N = 2778300

 = 2² x 3⁴ + 5² x 7³

Required factors are

(i) 4 x 694575 or (4 x (34 x 5² x 7³))

(ii) 81 x 34300 or (81 x (2² x 5² x 7³))

(iii) 25 x 111132 or (25 x (2² x 3⁴ x 7³))

(iv) 343 x 8100 or (343 x (2² x 3⁴ x 5²))

(v) 324 x 8575

(vi) 100 x 27783

(vii) 1372x 2025

(viii) 2778300 x 1

Total possible factors = 8