A positive integer 'n' is such that it's only digits are 3's. 'n'is exactly divisible by 383. When n/383 is divided by 1000, what is the remainder?
A. 351
B. 781
C. 651
D. 931
Answers
Answer:
Option (C), 651 is the correct answer.
Step-by-step explanation:
383 and 1000 are relatively prime because 383 has no factors of 2 or 5.
Doing so gives (383)^(-1) = 47 (mod 1000). We can see that 383*47 = 18001 = 1 (mod 1000).
A number n whose digits are 3's which is divisible by 383 should be larger than 333.
So, n mod 1000 = 333.
Now
(n/383) mod 1000
= (n * (383)^(-1)) mod 1000
= 333 * 47 mod 1000
= 15651 mod 1000
= 651
Answer:
651
Step-by-step explanation:
383 and 1000 are relatively prime because 383 has no factors of 2 or 5.
Doing so gives (383)^(-1) = 47 (mod 1000). We can see that 383*47 = 18001 = 1 (mod 1000).
A number n whose digits are 3's which is divisible by 383 should be larger than 333.
So, n mod 1000 = 333.
Now
(n/383) mod 1000
= (n * (383)^(-1)) mod 1000
= 333 * 47 mod 1000
= 15651 mod 1000
= 651