GCD of the years

Any number dividing $2016$ and $2015$ must also divide their difference so:

$gcd(2015,2016) \vert (2016-2015) \Rightarrow gcd(2015,2016) \vert 1$

$gcd(2015,2016)=\boxed{1}$

We have to find $\gcd(2015 , 2016)$ .
$2015 = 5 × 13 × 31$
$2016 = 2^5 × 7 × 3^2$
No, factor is common in them.
So, the greatest common divisor is $\color{#69047E}{\boxed{1}}$ because 1 is a factor of every number.

As Both Numbers Are Consecutive They Cannot Have Any Common Factor.

2016 = 2015 × 1 + 1

2015 = 1 × 2015 + 0

Thus by using Euclid's Lemma,

HCF = 1.

In case of co prime numbers their gcd is 1

co prime numbers are 1) prime numbers or their powers e.g. 5 and 11 or 25 and 121

, 2) consecutive numbers, e.g. 4, 5. 24, 25

2015 and 2016 are co prime consecutive numbers there gcd is 1

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