Math Story : Highest Common Factor (HCF)

Cirha’s Plantation

“This is bad! Without food, our people will die”, says Cirho. Samper town is facing the worst drought of their time and everybody is stressed. Can you think of a way to help the kids and people of Samper town?

“Idea! How about we plant vegetables and fruits? Later, we could distribute them to people in need. Once the seeds are planted, we can use Uncle Science’s latest technology to grow them faster. What do you think?” suggests Cirha. Her favourite hobby of gardening can actually save the needy. 

“Perfect!” says Squarho. “Let us divide the plantation task so that we can grow more variety and extra quantity”, says Triho. Everybody agrees. Cirha and Triho decide to grow two vegetables each. Squarho and Cirho decide to grow two fruits each. 

They go and get the seeds to start the plantation. 

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Cirha is in her garden with the seeds. “I have 12 spinach seeds and 20 tomato seeds. If I plant an equal number of seeds in each row, the plantation will look neat as well and I will be able to count faster. But how do I divide my seeds such that each row has an equal number of seeds and no seeds are left?” says Cirha. She decides to try various combinations. 

She starts by placing 3 seeds in each row. 12 spinach seeds easily get divided into 4 rows with each row having 3 seeds. But 20 tomato seeds do not get equally divided into 3 seeds. 

She then tries placing 5 seeds in each stack. Again 20 seeds get equally divided into 5 rows with 4 seeds each. But 12 does not get equally divided with 5. “This is so time taking and confusing! What should I do now?” she thinks. 

She tries and tries and tries various combinations. But cannot find an ideal one. A lot of time has already been wasted and she is disappointed. 

“Hey Cirha!” says a voice. She turns around to find who it is. “Oh! Uncle Math. I am so glad you’re here”, she says. “Of course. I heard about your plantation initiative so came over to see how is it going”, says Uncle Math. “It is going bad,” she says and explains her problem. 

“Haha! To divide the seeds such that they are equally arranged in rows and nothing is left, you need HCF”, says Uncle Math. “HCF? Is it some kind of secret code?” jokes Cirha. “HCF stands for Highest Common Factor. As the name indicates, it is the highest number from the list of common factors of given two or three numbers”, he says. 

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Cirha is still confused. “Alright! Let me explain you”, he says and grabs a board. He then asks her,” What are the factors of 12?” Cirha thinks for a while and says,“ factors divide the given number such that there is no remainder. So factors of 12 are 2, 3, 4, 6, 1, 12.” 

Cirha is right. Similarly, can you help her write the factors of 20 as well? 

Yes, the factors of 20 are 2, 4, 5, 10, 1, and 20.   

“Can you pick the common factors of both the numbers?” he asks. “2 and 4”, answers Cirha. “Clearly, 4 being the highest of all the common factors becomes the HCF of 12 and 20”, explains Uncle Math. “But if I divide the seeds in 2, even then I would be able to divide the seeds equally right. Then why 4 only?” she asks. 

“Good question. Yes, you will be able to divide equally using 2, but that might take a lot of time and might lead to confusion when you count them”, explains Uncle Math. “Oh! So that means if I plant 4 seeds in each row, I will be able to plant them equally without leaving any seeds behind. Woohoo!” says excited Cirha. Uncle Math agrees and helps her in planting the seeds. 

Cirha’s plantation looks great. She has used 5 rows to grow her tomatoes with each row having 4 seeds. She has used 3 rows to grow spinach with each row having 4 seeds. Now it is time to use Uncle Science’s advanced technology that grows the seeds into plants in just one day. 

“Hurrah! These look so beautiful and fresh”, says Cirha. It is time to pack them for the distributions. 

Triho, Squaro and Cirho are also back with their vegetables and fruits. “Cirha, your veggies look so fresh”, compliments Squarho. Cirha smiles and asks everyone to start the distributions as soon as possible. 

Together, they help many people in the town. Where there is a will, there is a way indeed.

We Learnt That…

  • Factors divide a given number such that there is no remainder.
  • HCF stands for Highest Common Factor. It is the highest number from the list of common factors of given two or three numbers.
  • We always use HCF to equally divide the number such that there is no leftover.
  • Where there is a will, there is a way.

Let’s Discuss

  • What is Samper town facing?
  • How did we decide to help the people in need?
  • Why was Cirha upset?
  • How did she divide her seeds equally?
  • What is HCF? Explain with an example.
  • What do you understand by this: “Where there is a will, there is a way.”

Please refer this guide by Fun2Do Labs for teaching HCF to kids :