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**Given that,**

**For any integer n, 6|n if and only if 2|n and 3|n.**

**6|n is means n is divisible by 6.**

**So from the given statement we need to prove, if n is divisible by 6 if and only if n is divisibly by 2 and n is divisible by 3.**

**we know that 6 = 2 * 3**

**6k = (2*3)k where k = 1, 2, 3, 4, ….**

**So anything is multiple of 6 is divisible by both 2 and 3.**

** which means if n is divisible by 6 then it will definitely divisible by both 2 and 3.**** **

**Let assume n is divisible by both 2 and 3.**

**So n = 2m * 3r****n = 6 * m * r**

**So n is also divisible by 6.**** **** ****Hence proved.**

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