(Q). Let p be the number of factors of 3000 & q be the number of factors of 4000 & r be the number of common factors of 3000 and 4000. Then find the ratio of (p-r):(q-r)
Solution:-
3000 = 3×10×10×10 = 2³×3¹×5³
∴ p = (3+1)(1+1)(3+1)
= 32
& 4000 = 4×10×10×10 = 2⁵×5³
∴ q = (5+1)(3+1) = 24
H.C.F. of 3000 & 4000 is 1000 = 10×10×10 = 2³×5³
∴ r = (3+1)(3+1) = 16
∴ (p-r):(q-r) = (32-16):(24-16)
= 16:8 = 2:1 Answer
