Odd integer A is a multiple of 3.
When 11573 is divided by A, remainder is 23 and when 6940 is divided by A, the remainder is 10.
Find all integers applicable to these conditions.
Answer
33, 105, 165, 231, 1155
Solution
When 11573 is divided by A, remainder is 23 and when 6940 is divided by A, the remainder is 10.
11573 - 23 = 11550, 6940 - 10 = 6930.
A is a common measure of 11550 and 6930.
The greatest common denominator of 11550 and 6930 is 2310 and 2310= 2 × 3 × 5 × 7 × 11. Since A is odd integer and a multiple of 3, it can be considered that A = 3 × 5, 3 × 7, 3 × 11, 3 × 5 × 7, 3 × 5 × 11, 3 × 7 × 11, 3 × 5 × 7 × 11 = 15, 21, 33, 105, 165, 231, and 1155.
Since A is a number larger than 23, 15 and 21 are not applied.
They are five numbers, 33, 105, 165, 231, and 1155.
When 11573 is divided by A, remainder is 23 and when 6940 is divided by A, the remainder is 10.
Find all integers applicable to these conditions.
Answer
33, 105, 165, 231, 1155
Solution
When 11573 is divided by A, remainder is 23 and when 6940 is divided by A, the remainder is 10.
11573 - 23 = 11550, 6940 - 10 = 6930.
A is a common measure of 11550 and 6930.
The greatest common denominator of 11550 and 6930 is 2310 and 2310= 2 × 3 × 5 × 7 × 11. Since A is odd integer and a multiple of 3, it can be considered that A = 3 × 5, 3 × 7, 3 × 11, 3 × 5 × 7, 3 × 5 × 11, 3 × 7 × 11, 3 × 5 × 7 × 11 = 15, 21, 33, 105, 165, 231, and 1155.
Since A is a number larger than 23, 15 and 21 are not applied.
They are five numbers, 33, 105, 165, 231, and 1155.
