palying with numbers -other rules of divisibility -post 8

Good morning boys, this is your 8th lesson. The topic for today is other rules of divisibility.

1. if a number is divisible by another number, then it is divisible by each of the other factors of that number.
Eg. 9 is a factor of 18.
       3 is a factor of 9.
Therefore 3 and 9 are both factors of 18.

Take 2 is a factor of 6 and it also divides 18, therefore 2,3,6,9 are factors of 18.

2. if a number is divisible by 2 co prime numbers then it is divisible by its product.
Eg. 80 is divisible by 5 and 4.
So, its is divisible by 5 X 4= 20 also,
80 is divisible by 5X2 =10 also 

3. If 2 given numbers are divisible by a number then their sum is also divisible by the number.
Eg. 16 and 20 are divisible by 4
So, 16+20=36 is also divisible by 4
16 and 20 are divisible by 2.
16+20=36, is also divisible by 2.

4.If 2 given numbers are divisible by a number then their difference is also divisible by that number.
Eg. 35 and 20 are divisible by 5. 
      35-20=15 is divisible by 5
      so these were other rules of divisibility.

Now lets do EX3.5 on page 61, Q1 
1. if a number is divisible by 3 it must be divisible by 9=(false).
Eg.3,21,6 are divisible by 3 but not by 9.

2. if divisible by 9, also by 3(yes).
Eg. 9,18,27,36 are divisible by 9 and 3.

3.if a number is divisible by 18 it is divisible by 3 and 6 (true).
Eg. 18 is divisible by 3 and 6.

4. if a number is divisible by 9 and 10 then it is divisible by 90.(true).
because both 9 and 10 are co prime numbers and a factor of 90.

5. If 2 numbers are co prime then one number must be a prime. (true).
Eg. 4 and 5 
      11 and 18.

6. All numbers divisible by 4 are divisible by 8 (false).
Eg. 4,12 and 20 are divisible by 4 and not by 8.

7. All numbers divisible by 8 must be divisible by 4 (true). As 4 is a factor of 8.


You may now do Q1 h and i on your own for homework.

look at Q10 determine if 25110 is divisible by 45(answer: yes)
9 and 5 are co prime numbers.
25110  / 9 =2790.
25110 / 5 = 5022.

You could now do Q11 on your own.
This is all for today, have a good day.

ANSWER TO Q11.
 Here ,the two given numbers are not co-primes. So, it is not necessary that a number divisible by both 4 and 6 ,must be divisible by their product 4x6=24

Example: 36 and 60 are divisible by both 4 an6 but not by 24.