- Highest Common Factor (H.C.F.) of two numbers = 44
- Least Common Multiple (L.C.M.) of two numbers = 264
- Quotient when the first number is divided by 2 = 44
- Remainder when the first number is divided by 2 = 0


The other number



Since the quotient when the first number is divided by 2 is 44 and the remainder is 0, we can conclude that the first number is a multiple of 2. Therefore, the first number can be written as 2 multiplied by some other number.

Let's assume the other number as 'x'. So, the first number can be written as 2x.


We know that the H.C.F. of two numbers is the highest number that divides both the numbers.

So, if we divide both the numbers by their H.C.F., we should get two relatively prime numbers (i.e., numbers with no common factors).

Let's divide the first number (2x) and the other number (x) by the H.C.F. (44):

- The first number (2x) divided by 44 will give x/22
- The other number (x) divided by 44 will give x/44

Since the H.C.F. is 44, x/22 and x/44 are relatively prime numbers.


We know that the L.C.M. of two numbers is the smallest number that is divisible by both the numbers.

Since the L.C.M. is 264, we can write the following equation:

L.C.M. = (H.C.F.) * (x/22) * (x/44)

Simplifying this equation, we get:

264 = 44 * (x/22) * (x/44)

Cancelling out the common factors, we get:

264 = x * x
264 = x^2


To find the value of x, we need to solve the quadratic equation:

x^2 = 264

Taking the square root of both sides, we get:

x = ±√264

Since we are looking for a positive value of x, we take the positive square root:

x = √264

Simplifying this, we get:

x = √4 * √66
x = 2 * √66


Now that we know the value of x, we can find the other number by substituting it back into the equation:

Other number = x = 2 * √66


Therefore, the other number is 2 * √66, which is approximately equal to 16.24.