If the highest common factor (HCF) and least common multiple (LCM) of two numbers are 33 and 264 respectively, and the first number divided by 2 gives a quotient of 33, what is the other number?

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To solve this problem, we first need to define some key terms and relationships between the numbers involved.

We know:

  • The HCF of the two numbers is 33.
  • The LCM of the two numbers is 264.
  • The first number (let’s call it A) divided by 2 yields a quotient of 33.

The relationship between two numbers and their HCF and LCM is given by the formula:

A × B = HCF × LCM

Where A and B are the two numbers. Now, let’s find A first:

Since when A is divided by 2 the quotient is 33, we can express this as:

  • A / 2 = 33

Multiplying both sides by 2 gives:

  • A = 33 × 2
  • A = 66

Now that we have the value of A, we can substitute it into the relation between A and B:

A × B = HCF × LCM

Substituting the values we know:

  • 66 × B = 33 × 264

Calculating the right side:

  • 33 × 264 = 8712

This gives us:

  • 66 × B = 8712

To find B, we divide both sides by 66:

  • B = 8712 / 66

Now performing the division:

  • B = 132

Thus, the other number B is 132.

In summary, if the highest common factor (HCF) and least common multiple (LCM) of two numbers are 33 and 264 respectively, and dividing the first number by 2 gives 33, then the other number is 132.

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