Mathematics - Permutation & Combination Question with Solution | TestHub

If $n$ is $\mathrm{a}+\mathrm{ve}$ number.

$n=P_1^{k_1}\cdot P_2^{k_2}\dots P_r^{k_r}$

(where $p_1,p_2,p_3,\dots .p_r$ are prime number) then number of divisors of $n$ are

$=\left(k_1+1\right)\left(k_2+1\right)\dots \left(k_r+1\right)$

∴ Number of prime factor of 6912 are $=2^8.3^3$ so no. of divisors $=9\times 4=36$

Prime factors of 52,400 are $=3^8\times 2^3$

∴ No. of divisors $=9\times 4=36$

Prime factors of 32,000 are $=5^3\times 2^8$

∴ No. of divisors $=9\times 4=36$

Now each number having same number of divisors i.e., 36,36,36

Each and every term is constant & constant sequence is always in A.P.& G.P. both as common difference is 0 and common ratio is 1 .