Question

The product of two numbers is 12960 and their HCF is 36. How many pairs of such numbers can be formed?

Answer 1

there are two pair of such number because 36a×36b=12960 so a×b=10 after it we break 10 in those factor which have hcf 1 so (1,10)and (2,5)

Answer 2

Answer:

Two pairs of such numbers can be formed.

Step-by-step explanation:

Given : The product of two numbers is 12960 and their HCF is 36.

To find : How many pairs of such numbers can be formed?

Solution :

We know that,

$\text{Product of the two numbers}=HCF\times LCM$

The product of two numbers is 12960.

The HCF is 36.

$12960=36\times LCM$

$LCM=\frac{12960}{36}$

$LCM=360$  ....(1)

Let the two numbers be 36a and 36b,

where, 'a' and 'b' are co-prime

LCM of the numbers 36a and 36b is 36ab.

Substitute in (1),

$36ab=360$

$ab=10$

The possible pairs of numbers are (1, 10), (2, 5)  whose product is 10.

Therefore, Two pairs of such numbers can be formed.