Name: Introduction to Modulus Function Ix|
Uploaded: 2019-07-19
Duration: 2 min 28 s
Description: Absolute value means the magnitude of a real number without regard to its sign. Watch this video to learn about the absolute value function called the modulu...

Question

Show that the product of three consecutive integers is divisible by

6

.

Accepted Answer

Let the three consecutive integers be $n, n + 1 and n + 2$ .

Whenever a number is divided by $3$ , the remainder obtained is either $0, 1$ or $2$ .

Therefore, $n = 3 p or 3 p + 1 o r 3 p + 2$ , where $p$ is some integer.

If $n = 3 p$ , then $n$ is divisible by $3$ .

If $n = 3 p + 1$ , then $n + 2 = 3 p + 1 + 2 = 3 p + 3 = 3 (p + 1)$ is divisible by $3$ .

If $n = 3 p + 2$ , then $n + 1 = 3 p + 2 + 1 = 3 p + 3 = 3 (p + 1)$ is divisible by $3$ .

So, we can say that one of the numbers among $n, n + 1 and n + 2$ is always divisible by $3$ that is:

$n (n + 1) (n + 2)$ is divisible by $3$ .

Similarly, whenever a number is divided by $2$ , the remainder obtained is either $0 or 1$ .

Therefore, $n = 2 q or 2 q + 1$ , where $q$ is some integer.

If $n = 2 q$ , then $n$ and $n + 2 = 2 q + 2 = 2 (q + 1)$ is divisible by $2$ .

If $n = 2 q + 1$ , then $n + 1 = 2 q + 1 + 1 = 2 q + 2 = 2 (q + 1)$ is divisible by $2$ .

So, we can say that one of the numbers among $n, n + 1 and n + 2$ is always divisible by $2$ .

Since, $n (n + 1) (n + 2)$ is divisible by $2$ and $3$ .

Hence, $n (n + 1) (n + 2)$ is divisible by $6$ .

Show that the product of three consecutive integers is divisible by $6$ .

Important Questions on Number System

Learn and Prepare for any exam you want !

Show that the product of three consecutive integers is divisible by 6.

Important Questions on Number System

Learn and Prepare for any exam you want !

Show that the product of three consecutive integers is divisible by $6$ .