Question

Prove that 7^7-7^6 is divisible by 6

Answer 1

To prove that 7^7-7^6 is divisible by 6, we need to show that it leaves no remainder when divided by 6.

We can factor out 7^6 from the expression to get:

7^7-7^6 = 7^6(7-1)

Simplifying this expression, we get:

7^7-7^6 = 7^6(6)

We can see that the expression is a multiple of 6, which means that it is divisible by 6. Therefore, we have proved that 7^7-7^6 is divisible by 6.

Answer 2

To prove that 7^7 - 7^6 is divisible by 6, we can factor out 7^6 from the expression:

7^7 - 7^6 = 7^6 (7 - 1)

Simplifying the expression, we get:

7^7 - 7^6 = 7^6 (6)

We can see that 7^6 is a common factor in the expression, and 6 is also a factor. Therefore, we can conclude that 7^7 - 7^6 is divisible by 6.

Explanation: