Number System#!#Divisibility Criteria

A number is divisible by 6 if it is divisible by

Which of the following statements are true? If a number is divisible by 3, it must be divisible by 9. If a number is divisible by 9, it must be divisible by 3. If a number is divisible by 4, it must be divisible by 8. If a number is divisible by 8, it must be divisible by 4. If a number is divisible by 18, if it is divisible by both 3 and 6. If a number is divisible by both 9 and 10, it must be divisible by 90. If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately. If a number divides three numbers exactly, it must divide their sum exactly. If two numbers are co-prime, at least one of them must be a prime number. The sum of two consecutive odd numbers is always divisible by 4.

Property 1 If a number is divisible by another number then it is divisible by each of the factors of that number.If abc are three natural numbers such that a is divisible by b and b is divisible by c then a is divisible by c also.

Which of the following statements are true? If a number divisible by 3, it must be divisible by 9. If a number is divisible by 9, it must be divisible by 3. If a number is divisible by 4, it must be divisible by 8. If a number id divisible by 8,it must be divisible by 4. A number is divisible by 18, if it is divisible by both 3 and 6. If a number divisible by both 9 and 10, it must be divisible by 90.

If the sum of digits of a number is divisible by three, then the number is always divisible by

Write (T) for true and (F) for false against each of the following statements : (i) If a number is divisible by 4. it must be divisible by 8 . (ii) If a number is divisible by 8 . it must be divisible by 4 . (iii) If a number divides the sum of two number exactly. it must exactly divide the num .bers separately. (iv) If a number is divisible by both 9 and 10 . it must be divisible by 90. (v) A number is divisible by 18 if it is divisible by both 3 and 6 . (vi) If a number is divisible by 3 and 7 . it must be divisible by 21. (vii) The sum of two consecutive odd number is always divisible by 4 . (viii) If a number divides two number exactly. it must divide their sum exactly.

Which of the following statements are true? (a) If a number is divisible by 3, it must be divisible by 9. (b) If a number is divisible by 9, it must be divisible by 3. (c) A number is divisible by 18, if it is divisible by both 3 and 6. (d) If a number is divisible by 9 and 10 both, then it must be divisible by 90. (e) If two numbers are co-primes, at least one of them must be prime. (f) All numbers which are divisible by 4 must also be divisible by 8. g) All numbers which are divisible by 8 must also be divisible by 4. (h) If a number exactly divides two numbers separately, it must exactly divide their sum. (i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.