Any two consecutive numbers are coprime.
Step 1: What are consecutive numbers?
Consecutive numbers come one after another, like 7 and 8, or 20 and 21. They differ by 1.
Step 2: What does coprime mean?
Two numbers are coprime if their HCF (also called GCD) is 1.
Step 3: Write the two numbers
Let the two consecutive numbers be \( n \) and \( n+1 \).
Step 4: Think about a common factor
Suppose a number \( d \) divides both \( n \) and \( n+1 \).
Then \( d \mid n \) and \( d \mid (n+1) \).
Step 5: Use the difference
If \( d \) divides both, it must also divide their difference:
\((n+1) - n = 1\).
So \( d \mid 1 \).
Step 6: Only one possibility
The only positive divisor of \( 1 \) is \( 1 \) itself.
So \( d = 1 \).
Step 7: Conclusion
The greatest common factor of \( n \) and \( n+1 \) is \( 1 \).
Therefore, any two consecutive numbers are coprime.
Quick examples
\( \gcd(7,8)=1 \), \( \gcd(20,21)=1 \), \( \gcd(35,36)=1 \).