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The HCF of two numbers is 8 and the product of the two numbers is 6400. How many pairs of numbers exist, which satisfy the above conditions?

The HCF of two numbers is 8 and the product of the two numbers is 6400. How many pairs of numbers exist, which satisfy the above conditions? Correct Answer 2

Given:

The HCF of two numbers is 8 and the product of the two numbers is 6400.

Concept used:

HCF of two or more numbers is the greatest factor that divides the numbers.

Calculation:

Since the HCF of the aforementioned numbers is 8, let the two numbers be 8P and 8Q respectively. (Where P and Q are co-prime to each other)

According to the question,

8P × 8Q = 6400

⇒ PQ = 6400/64

⇒ PQ = 100

Now, 100 = 22 × 52

Thus, the only possible co-prime pairs are (1, 100) and (4,25).

∴ Only two pairs of numbers exist, which satisfy the above conditions.

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