If you add 1 to a number, it will be divisible by 6; if you add 3 to it, it will be divisible by 8; if you add 5 to it, it will be divisible by 10 We also know that this number is divided into 6, 8 and 10, and the sum of the quotients is 235. What is the maximum of this number?

If you add 1 to a number, it will be divisible by 6; if you add 3 to it, it will be divisible by 8; if you add 5 to it, it will be divisible by 10 We also know that this number is divided into 6, 8 and 10, and the sum of the quotients is 235. What is the maximum of this number?

Let: this number be x, a, B, C, which are positive integers. X + 1 = 6A (add 1 to it, you can divide by 6) x + 3 = 8b (add 3 to it, you can divide by 8) x + 5 = 10C (add 5 to it, you can divide by 10) x / 6 = A-1 / 6 = a-1-5 (the remainder cannot be negative) x / 8 = B-3 / 8 = b-a-5x / 10 = C-5 / 10 = c-1-5, so quotient