- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# 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.

To do:

We have to find which of the given statements is true.

Solution :

(a) We know that,

If a number is divisible by another number, it is divisible by its factors.

Therefore,

If a number is divisible by 9 it is divisible by 3 but the converse is not necessarily true.

For example,

12 and 15 are divisible by 3 but not by 9.

Therefore, if a number is divisible by 3 it may not be divisible by 9.

The given statement is false.

(b) We know that,

If a number is divisible by another number, then it is divisible by its factors.

Therefore,

If a number is divisible by 9 it is divisible by 3

The given statement is true.

(c) A number is divisible by 18 if it is divisible by both 9 and 2.

The given statement is false.

(d) A number is divisible by 90 if it is divisible by both 9 and 10.

The given statement is true.

(e) When two numbers have no common factors other than 1, then the numbers are co-prime.

8 and 9 are co-primes but both 8 and 9 are not prime numbers.

(f) For example,

12 is divisible by 4 but is not divisible by 8.

Therefore, the given statement is false.

(g) 4 is a factor of 8.

This implies,

All numbers which are divisible by 8 must also be divisible by 4.

Therefore, the given statement is true.

(h) For example,

2 divides 6 and 10.

$6 + 10 = 16$

$16$ is also divisible by 2.

Therefore, the given statement is true.

(i) $10+30=40$ is divisible by 4 but both 10 and 30 are not divisible by 4.

The given statement is false.

- Related Questions & Answers
- Check if a large number is divisible by 9 or not in C++
- Rearrangement of a number which is also divisible by it in C++
- Check if a large number is divisible by 3 or not in java
- Check if a large number is divisible by 3 or not in C++
- Check if a large number is divisible by 20 in C++
- Check if any permutation of a number is divisible by 3 and is Palindromic in Python
- Check if N is divisible by a number which is composed of the digits from the set {A, B} in Python
- Find if a number is divisible by every number in a list in C++
- Number of digits to be removed to make a number divisible by 3 in C++
- Check if a number is divisible by 23 or not in C++
- Check if a number is divisible by 41 or not in C++
- Find permutation of n which is divisible by 3 but not divisible by 6 in C++
- Write a C# program to check if a number is divisible by 2
- Check if a number is divisible by all prime divisors of another number in C++
- Check if a large number is divisible by 11 or not in java
- Check if a large number is divisible by 13 or not in C++