highest common factor working model – hcf and lcm – diy – maths project – tlm

Creating a working model to demonstrate the concept of finding the Highest Common Factor (HCF) using syringes and cardboard can be an interesting and interactive project.

Here’s a simple and easy DIY (Do It Yourself) project for understanding HCF and LCM (Lowest Common Multiple):

Materials Needed:

  1. Cardboard
  2. Syringes (2 or more)
  3. Plastic tubing (cut into equal lengths)
  4. Water or colored liquid (for visibility)
  5. Funnel
  6. Markers
  7. Ruler
  8. Scissors
  9. Glue or tape
  10. Labels or index cards

Steps to Create the HCF Working Model:

Step 1: Prepare the Base:

  • Cut a large piece of cardboard to use as the base for your working model.

Step 2: Syringe Setup:

  • Attach plastic tubing to the nozzles of each syringe. The tubing should be long enough to reach a common point on the cardboard.

Step 3: Mark the Syringes:

  • Use markers to label each syringe with a number representing a factor. For example, if you are finding the HCF of 45 and 60, label one syringe with ’45’ and the other with ’60.’

Step 4: Fill the Syringes:

  • Fill each syringe with water using a funnel. The water level should represent the corresponding number on the syringe.

Step 5: Display on Cardboard:

  • Attach the syringes to the cardboard, placing them side by side. Make sure the tubing reaches a common point.

Step 6: Find the HCF:

  • Gradually press the plunger of each syringe until the water reaches its lowest level.
  • Observe where all the water levels align at the same point. This point represents the HCF.

Step 7: Optional – Label the HCF:

  • Use labels or index cards to label the common point as the Highest Common Factor.


  • Explain that the water levels in the syringes represent the factors of the given numbers.
  • Demonstrate how by adjusting the water levels, you can find the HCF where all the levels align.

Extension – LCM:

  • If you want to demonstrate LCM as well, you can add more syringes and tubes for additional numbers.
  • Show how the LCM is the value when all syringes reach their maximum levels simultaneously.

This DIY working model provides a hands-on way for students to understand the concept of HCF and LCM using syringes and water levels. It offers a visual and interactive representation, making it an effective Teaching-Learning Material (TLM) for mathematical concepts.

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