What least number must be subtracted from 1672 to obtain a number which is completely divisible by 17?

1. Break Down the Problem

To find the least number that must be subtracted from 1672 to make it divisible by 17, we need to determine the remainder when 1672 is divided by 17.

2. Relevant Concepts

We will use the concept of division and the remainder: $\text{Remainder} = \text{Number} - (\text{Quotient} \times \text{Divisor})$

3. Analysis and Detail

1. Calculate the division of 1672 by 17: $1672 \div 17 = 98.353 \quad (\text{take the integer part})$ The quotient is 98.

2. Calculate the product of the quotient and the divisor: $98 \times 17 = 1666$

3. Determine the remainder: $\text{Remainder} = 1672 - 1666 = 6$

4. The least number to subtract is equal to the remainder found: $\text{Least number} = 6$

4. Verify and Summarize

To verify, we can subtract 6 from 1672 and check the divisibility: $1672 - 6 = 1666$ Now, check if 1666 is divisible by 17: $1666 \div 17 = 98$ Since there is no remainder, 1666 is divisible by 17.

Final Answer

The least number that must be subtracted from 1672 to obtain a number that is completely divisible by 17 is 6.