Divisible by just one more

Number Theory Level 1

Let $x$ be a positive integer such that

Which of the following must be true as well?

4x

is divisible by 5

5x

is divisible by 6

6x

is divisible by 7

7x

is divisible by 8

1 solution

Jordan Cahn
Nov 12, 2018

If $2x$ is divisible by $3$ then $x$ must be divisible by $3$ .

If $3x$ is divisble by $4$ then $x$ must be divisible by $4$ (and also $2$ .

If $x$ is divisible by both $2$ and $3$ , then it must also be divisible by $6$ . So $5x$ is divisible by $6$ .