Question

Which of the statement(s) is/are false?

• A. If a number ‘a' is divisible by another number 'b', then it is divisible by each of the factors of that number 'b'.
• B. If 'a’ and ‘b’ have no common factors (other than unity), the number divisible by ‘a’ and ‘b’ is also divisible by a × b.
• C. If two given numbers are divisible by a number, then their sum is also divisible by that number.
  
• D. None of these

Answer 1

The correct option is D None of these

Consider a factor of 24, say 12.
Factors of 12 are 1, 2 ,3, 4, 6, 12.
24 is divisible by 2, 3, 4, 6, we can say that 24 is divisible by all factors of 12.
$\therefore$ First statement is true.

60 is divisible by 3 and 5 which have no common factors each other. 60 is also divisible by 3 × 5 = 15.
$\therefore$ Second statement is true.

Let us take two numbers 16 and 20. These numbers are both divisible by 4. The number 16 + 20 = 36 is also divisible by 4.
$\therefore$ Third statement is true.

None of them are false.