Correct Answer - Option 3 : 2

Given:

HCF = 4

LCM = 400

Concept used:

If the number a = 4x and b = 4y, then HCF = 4

Where x and y will be the co-prime.

**Formula used:**

LCM × HCF = a × b

Calculation:

HCF is 4. So numbers are multiples of 4

Let the numbers be 4x and 4y.

LCM × HCF = a × b

⇒ 400 × 4 = 4x × 4y

⇒ 1600 =16xy

⇒ xy = 100

Here, x and y will be the co-prime.

Then, possible pairs are (1, 100), (4, 25)

∴ There will be 2 such possible pairs.