Choose any 3 numbers. When is their sum divisible by 3? Explore all possible cases and generalise. Class 8

Choose any 3 numbers. When is their sum divisible by 3? Explore all possible cases and generalise. Class 8

Question 1.

Choose any 3 numbers. When is their sum divisible by 3? Explore all possible cases and generalise. Class 8

Solution:

Their sum will be divisible by 3, if the sum of the digits of this sum is divisible by 3. In some cases, it will be divisible by 3. But in the case of three consecutive numbers, the sum will always be divisible by 3.

Question 2.

Is the product of two consecutive integers always multiple of 2? Why? What about the product of three consecutive integers? Is it always a multiple of 6? Why or why not? What can you say about the product of 4 consecutive integers? What about the product of five consecutive integers? Class 8

Solution:

Yes, because out of two, one number is even. Yes, because out of three numbers one is divisible by 2 and one is divisible by 3. Product of four consecutive numbers will also be divisible by 4 and 8, in addition to 2, 3 and 6. Product of 5 consecutive numbers will also be divisible by 5, in addition to 2, 3, 6, 4 and 8.