MathematicsFind the HCF of the numbers given below:k, 2k, 3k, 4k and 5k where k is any positive integer.

Find the HCF of the numbers given below: $k$ , $2 k$ , $3 k$ , $4 k$ and $5 k$ where k is any positive integer.

We have to find the HCF of the numbers

k

2 k

3 k

4 k

and

5 k

, where k is any positive integer.
Consider the numbers and take k common,

k 1, 2, 3, 4, 5

.
Now, calculate the HCF of the numbers

1, 2, 3, 4, 5

as it is clear that there is no common factor other than 1.
∴

H C F = 1

So, HCF of the numbers

k

2 k

3 k

4 k

and

5 k

will be k times the HCF of numbers

1, 2, 3, 4, 5

.
⇒

H C F k, 2 k, 3 k, 4 k, 5 k = k × 1

⇒

H C F k, 2 k, 3 k, 4 k, 5 k = k

So, HCF of the numbers

k

2 k

3 k

4 k

and

5 k

is k.
Therefore, option (1) is correct.

JEE