To find the least number that must be added to 308 to make it divisible by 19, we need to determine the remainder when 308 is divided by 19, and then subtract this remainder from 19.

Step 1: Divide 308 by 19

Perform the division: $308 \div 19 \approx 16.21$ The quotient is 16, and the remainder can be found by calculating: $308 - (19 \times 16) = 308 - 304 = 4$ So, the remainder when 308 is divided by 19 is 4.

Step 2: Subtract the remainder from 19

To make 308 divisible by 19, we need to add the difference between 19 and the remainder. $19 - 4 = 15$

Final Answer:

The least number that must be added to 308 to make it divisible by 19 is 15.

Would you like a more detailed breakdown or have any questions? Here are some related questions you might find interesting:

1. How do you perform modulo operations to find remainders?
2. What is the concept of divisibility rules, and how can they be used efficiently?
3. How can we use the Euclidean algorithm to find the remainder of a division?
4. What happens if we subtract the remainder from the divisor in other scenarios?
5. How does this method work for larger numbers or divisibility by other primes?

Tip: When dividing to find remainders, the division can often be simplified by breaking down large numbers into smaller, manageable parts, especially when using modular arithmetic.