Question

8 and 3
7. The product of three consecutive numbers is always divisible by 6. Verify this state
with the help of some examples.
8. The sum of two consecutive odd numbers is divisible by 4. Verify this statemen
the help of some examples.​

Answer 1

Answer:

7)

1*2*3=61 which is divisible by 6

2*3*4=24 which is divisible by 6

example:

pick any three consecutive numbers.

One of them will be divisible by 3 (as we’re talking about 3 consecutive numbers), and at least one of them will be divisible by 2 (as for any 2 consecutive numbers, one will be even, and the other odd). For example

11 12 13 ← example of the number divisible by 3 not an even number

if the even number is divisible by 3, the number will be divisible by 6, and the multiplication with other numbers will still give a result divisible by 6

11*12*13 = 11*(6*2)*13 = 11*6*2*13 = 6*2*11*13

8 9 10 ← example of the number divisible by 3 not an even number

you can write one of the even numbers as twice its half, and the number divisible by 3 as 3 times its third

2*4 3*3 10

when you multiply all these numbers you can take the 2 and 3 together to form 6, and thus the result will be divisible by 6

8*9*10 = (2*4)*(3*3)*10 = 2*4*3*3*10 = (2*3)*4*3*10 = 6*3*4*10

8)

3+ 5 = 8 and 8 is divisible by 4.

5 + 7 = 12 and 12 is divisible by 4.

7+ 9 = 16 and 16 is divisible by 4.

9 + 11 = 20 and 20 is divisible by 4.

Example:

Take two odd numbers 3,5

3+5=8 here 8 is divisible by 4.

Example 2

Let two odd numbers 13,15

13+15=28 here 28 is also divisible by 4