Indices, SM-Bank 054 Using divisibility tests, find the smallest number greater than 1000 that is divisible by 6. (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only \(\text{See worked solution}\) Show Worked Solution \(\text{A number is divisible by }6\ \text{if it is divisible by both }2\ \text{and }3.\) \(\text{A number is divisible by }2\ \text{if the last digit is }2 , 4 , 6 , 8 , 0.\) \(\therefore\ \text{The first possible number is }1002\ \text{as it is divisible by }2\) \(\text{A number is divisible by }3\ \text{if the sum of the digits is divisible by }3.\) \(1+0+0+2=3\ \Rightarrow\ \text{divisible by 3}\ \checkmark\) \(\therefore 1002\ \text{is the smallest number greater than }1000\ \text{that is divisible by }6.\)