Question

show that if 8 positive integers are chosen, two of them will have the same remainder when divide by 7

Answer 1

Answer:

We require to show that if any eight positive integers are chosen, two of them will have the same remainder when divide by 7.

Construct seven different sets, each containing single number that is the remainder when divide by 7 as follows:

The remainder of each of the eight positive integer when divide by 7 must belong to one of these sets.

Step-by-step explanation:

Answer 2

Concept

Division is one out of the four basic arithmetic operations used in mathematics which is used to divide numbers and equations. When we divide something and it doesn’t completely divides the left one part is called as remainder.

For example 7 divided by 3 we get remainder 1

Find

If 8 positive integers are chosen, two of them will have the same remainder when divided by 7

Solution

We need to show that if any eight positive integers are chosen, two of them will have the same remainder when divide by 7.

So lets take an example

Numbers are 8,9,10,11,12,13,14,15

So Lets find remainder of each when divided by 7

Remainder of 8/7 = 1

Remainder of 9/7 = 2

Remainder of 10/7 = 3

Remainder of 11/7 = 4

Remainder of 12/7 = 5

Remainder of 13/7 = 6

Remainder of 14/7 = 0

Remainder of 15/7 = 1

When 8 and 15 are divided by 7 we get the same remainder which is 1.

So, When any eight positive integers are chosen, two of them will have the same remainder when divide by 7.

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