The document discusses various methods for determining prime numbers and the greatest common divisor (GCD) through algorithmic approaches. It details functions for checking primality and an explanation of the sieve of Eratosthenes for prime generation. Additionally, it provides a specific example of calculating the GCD of two numbers, 54 and 24.

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2. —Team GCC
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bool isPrime (int n)
{
for (int i=2; i<n; i++)
if (n%i==0)
return false;
return true;
}
( Simply traverse from 2 to 𝑛 − 1 )

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bool isPrime (int n)
{
if (n<=1) return false;
if (n==2) return true;
if (n%2==0) return false;
for (int i=3; i<n; i+=2)
if (n%i==0)
return false;
return true;
}
number not
divisible by 2 is
not divisible by
any even number

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bool isPrime (int n)
{
for (int i=2; i*i<n; i++)
if (n%i==0)
return false;
return true;
}
( Simply traverse from 2 to 𝑛 )

9. ALL prime numbers are of form 6𝑘 ± 1
FACT

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bool isPrime (int n)
{
if (i==2) return true;
if (i==3) return true;
for (int i=6; i*i<n; i+=6)
if (n%(i-1)==0)
return false;
else if (n%(i+1)==0)
return false;
return true;
}

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Basic concept - we pick one prime number and eliminate all the
multiples of that prime number
1. Create an array of 𝑛 + 1 elements (0,1,…,n)
2. Initialise the array with 1 (consider all as prime)
3. Mark 0 & 1 as 0 (!prime)
4. Iterate array till 𝒊 = 𝟏 (prime is found)
5. Mark all consecutive multiple of p as 0 (!prime)
6. Repeat step 4 & 5 till 𝑖 ≠ 𝑛

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void generatePrime (int n)
{
int isPrime[n+1];
for (int i=0; i<n; i++)
isPrime[i] = 1;
isPrime[0] = isPrime[1] = 0;
for (int i=2; i<n; i++)
if (isPrime[i]==1)
for (int j=i+i; j<n; j+=i)
isPrime[i] = 0;
}
Create an array of 𝑛 + 1 elements (0,1,…,n)Initialise the array with 1 (consider all as prime)Mark 0 & 1 as 0 (!prime)Iterate array till 𝑖 = 1 (prime is found)Mark all consecutive multiple of p as 0 (!prime)Repeat step 4 & 5 till 𝑖 ≠ 𝑛

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What is GCD of 54 and 24?
Divisor of 54: 1, 2, 3, 6, 9, 18, 27, 54
Divisor of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common divisor are: 1, 2, 3, 6
GCD (54, 24) = 6

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Homework :D

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https://en.wikipedia.org/wiki/Euclidean_algorithm
[video content removed]

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—pGxplorer
Keep practicing,
It’s a sport worth playing!

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THANK YOU