Question

5. Is 9 a factor of the following? (i) 394683 (ii) 1872546 (iii) 5172354

Answer 1

Answer:

  (i) no, remainder is 6

  (ii) no, remainder is 6

  (iii) yes

Step-by-step explanation:

A number is divisible by 9 when the sum of its digits is divisible by 9. (The process of computing the sum of digits is called "casting out 9s".) You can basically treat any 9 as though it were 0.

(i) 3+9+4+6+8+3 = 33, 3+3 = 6. The remainder from division by 9 is 6. 9 is not a factor.

__

(ii) 1 + 8 + 7 + 2 + 5 + 4 + 6 = 9 + 9 + 9 + 6 = 33, 3+3 = 6. The remainder from division by 9 is 6. 9 is not a factor.

__

(iii) 5 + 1 + 7 + 2 + 3 + 5 + 4 = 6 + 9 + 3 + 9 = 27 = 3×9. This is divisible by 9, so the number is divisible by 9. 9 is a factor.

Answer 2

Answer:

The answer is (iii) 5172354