Question

The HCF of two consecutive even numbers is:

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(4\)

Hint:

Consecutive integers are co-prime. For consecutive even numbers \(2n\) and \(2n+2\), a factor \(2\) is always common, so HCF \(=2\).

Answer 1

The Correct Option is C

Step 1: Represent consecutive even numbers.
Let the two consecutive even numbers be \(2n\) and \(2n+2 = 2(n+1)\).
Step 2: Take out the common factor.
\(\gcd(2n,\,2n+2)=\gcd\big(2n,\,2(n+1)\big)=2\cdot \gcd\big(n,\,n+1\big).\)
Step 3: Use property of consecutive integers.
\(\gcd(n,\,n+1)=1\) (consecutive integers are co-prime). Hence, the HCF is \(2\times 1=2\).