The-sum-of-all-the-divisors-of-24-is-60-Find-the-sum-of-all-the-divisors-of-24-79-

Question Number 202672 by BaliramKumar last updated on 31/Dec/23

The sum of all the divisors of 24 is 60 .

Find the sum of all the divisors of 24 \times 79 .

Answered by a.lgnaoui last updated on 31/Dec/23

60

Commented by BaliramKumar last updated on 31/Dec/23

sum of divisors of 1896 = ? [24 \times 79 = 1896]

Commented by Panav last updated on 31/Dec/23

61

Answered by MM42 last updated on 31/Dec/23

d ∣ 24 & Σ d = 60

d^{'} ∣ 79 & Σ d^{'} = 80

\Rightarrow Σ d^{″} = 4800 ✓; d^{″} ∣ 24 \times 79

Commented by BaliramKumar last updated on 31/Dec/23

yes

Commented by MM42 last updated on 31/Dec/23

l e t A = {d; d ∣ m} & B = {d^{'}; d^{'} ∣ n} & C = {d^{″}; d^{″} ∣ m n}; (m, n) = 1

\Rightarrow C = {1, d_{1}, \dots, d_{m}, d_{1}^{'}, \dots, d_{n}^{^{'}}, d_{1} d_{1}^{^{'}}, \dots, d_{m} d_{n}^{^{'}}}

\Rightarrow Σ d^{^{″}} = Σ d \times Σ d^{'}

Commented by BaliramKumar last updated on 31/Dec/23

yes sir

Answered by BaliramKumar last updated on 31/Dec/23

σ_{1} (24) = 60

σ_{1} (79) = 1 + 79 = 80

σ_{1} (24 \times 79) = 60 \times 80 = 4800

σ_{1} (a) = m σ_{1} (b) = n

σ_{1} (ab) = mn Hcf (a, b) = 1 & a \neq b