question_answer 1)

Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no)? Number Divisible by 2 3 4 5 6 8 9 10 11 (i) 128 Yes No Yes No No Yes No No No (ii) 990 (iii) 1586 (iv) 275 (v) 6686 (vi) 639210 (vii) 429714 (viii) 2856 (ix) 3060 (x) 406839

Answer:

                We know that, a number is divisible by 2, if it has digits 0, 2, 4, 6 or 8 in ones place. 3, if the sum of the digits is a multiple of 3 or it is, divisible by 3. 4, if last two digits of the number is completely divisible by 4. 5, if a number has 0 or 5 in its ones place. 6, if it is divisible by 2 and3 both. 8, if last three digits of the number is completely divisible by 8. 9, if the sum of the digits of the number is divisible by 9. 10, if a number has 0 in its ones place. 11, if the difference of sum of the digits of even place and, sum of the digits at odd place is either 0 or multiple of ll. Now, complete table is shown as below Number Divisible by 2 3 4 5 6 8 9 10 11 (i) 128 Yes No Yes No No Yes No No No (ii) 990 Yes Yes No Yes Yes No Yes Yes Yes (iii) 1586 Yes No No No No No No No No (iv) 275 No No No Yes No No No No Yes (v) 6686 Yes No No No No No No No No (vi) 639210 Yes Yes No Yes Yes No No Yes Yes (vii) 429714 Yes Yes No No Yes No Yes No No (viii) 2856 Yes Yes Yes No Yes Yes No No No (ix) 3060 Yes Yes Yes Yes Yes No Yes Yes No (x) 406839 No Yes No No No No No No No