The sum of all the divisors of 25 ⋅ 37 ⋅ 53 ⋅ 72 is

Question

The sum of all the divisors of 25 ⋅ 37 ⋅ 53 ⋅ 72 is (A) 26 ⋅ 38 ⋅ 54 ⋅ 73-2 ⋅ 3 ⋅ 5 ⋅ 7 (B) 26 ⋅ 38 ⋅ 54 ⋅ 73 (C) 26 ⋅ 38 ⋅ 54 ⋅ 73-1 (D) ((26-1)(38-1)(54-1)(73-1)/2.4 .6)

Tardigrade Admin · Accepted Answer

Correct answer is (d) ((26-1)(38-1)(54-1)(73-1)/2.4 .6)

Q. The sum of all the divisors of $2^{5} \cdot 3^{7} \cdot 5^{3} \cdot 7^{2}$ is

$2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 7^{3} - 2 \cdot 3 \cdot 5 \cdot 7$

$2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 7^{3}$

$2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 7^{3} - 1$

$\frac{( 2 ^{6} - 1 ) ( 3 ^{8} - 1 ) ( 5 ^{4} - 1 ) ( 7 ^{3} - 1 )}{2.4.6}$

Correct answer is (d) $\frac{( 2 ^{6} - 1 ) ( 3 ^{8} - 1 ) ( 5 ^{4} - 1 ) ( 7 ^{3} - 1 )}{2.4.6}$

Q. The sum of all the divisors of 25⋅37⋅53⋅72 is

26⋅38⋅54⋅73−2⋅3⋅5⋅7

26⋅38⋅54⋅73

26⋅38⋅54⋅73−1

2.4.6(26−1)(38−1)(54−1)(73−1)​