Subtract the sum of integers from 1 to 15 from the product of integers from 1 to 15.
When the quotient is divided by 154, find a remainder.
Answer
34
Solution
154 can be resolved into prime factors with 154 = 2 × 7 × 11.
Accordingly (Product of an integer from 1 to 15)/154 can be divided with no remainder.
Or it is considered that remainder is set to 154.
When the quotient is divided by 154, find a remainder.
Answer
34
Solution
154 can be resolved into prime factors with 154 = 2 × 7 × 11.
Accordingly (Product of an integer from 1 to 15)/154 can be divided with no remainder.
Or it is considered that remainder is set to 154.
Sum total from 1 to 15 is (1 + 15) × 15/2 = 120.
The remainder of 120/154 is 120.
The remainder of 120/154 is 120.
Therefore (remainder 154) - (remainder 120) = remainder 34.
