Sign in
Please select an account to continue using cracku.in
↓ →
Amicable numbers are a pair of distinct natural numbers (a, b) such that the sum of the proper divisors of a equals b and the sum of the proper divisors of b equals a. Given that (220, y) is a pair of amicable numbers, y equals:
220 = $$2^2\times5\times11$$
So, the Sum of all divisors = $$(2^0+2^1+2^2)(5^0+5^1)(11^0+11^1)$$
= (7)(6)(12)
= 504
Proper divisors are all the divisors except number itself .
So, the sum of all proper divisors = $$504-220$$ = 284.
Now to check if the (220,284) are amicable pair of numbers, we have to verify it with checking for sum of proper divisors for 284 :
284 = $$2^2\left(71\right)$$
So, the Sum of all divisors = $$(2^0+2^1+2^2)(71^0+71^1)$$
= (7)(72)
= 504
Therefore, no of proper divisors of 284 are = 504-284 = 220.
Hence, (220,284) are amicable pair of numbers.
Crack IPMAT 2026 with Cracku
Educational materials for IPMAT and IIMB UG preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.