Quant Question Of The Day : 2

Numbers

The number of divisors the form 4n +1, n ≥0, of the number 10¹⁰ × 11¹¹ × 13¹³
__________
A. 256
B. 924
C. 1024
D. 512
E. None of these

Solution : 10¹⁰ × 11¹¹ × 13¹³

= 2¹⁰ × 5¹⁰ × 11¹¹ × 13¹³ has the divisors are of the form 2^a × 5^b × 11^c × 13^d

Where a = 0 , 1,2, 3, ……, 10.

b = 0, 1, 2, 3 ……, 10

c = 0, 1, 2, 3, ……, 11.

d = 0,1, 2, 3,….., 13.

It is of the form 4n + 1 if a = 0 .

b = 0,1,2,3……., 10

c = 0,2, 4 , 6,…., 10

d = 0, 1, 2, 3 , ….13.

Hence , 11 × 6 ×14 = 924 factors.