Math Story : Introduction To Factors

Fun With Factors

“Atriho! You will lead this attack. Remember, none of our army members must be left alone,” says Uncle Bad. Atriho Boss carefully listens to his instructions and leaves. 

“Hail Atriho Boss! Hail Uncle Bad! We will make everyone sad!” says the army. Atriho is ready for another attack. This time he has a different plan. Will his strategy work this time? 

“There are 20 members in the army. If I arrange them in such a way that none of the members is left, we will get various shapes and positions for attack. The enemy will not be able to predict our next move. HaHa! This is perfect!” he says to himself. It looks like he is confident about his new strategy. 

On the other side, Uncle Math and the kids decide to send Mr Gadget so that he can produce new gadgets to face the villain army. 

It is the attack day. Atriho Boss and his army charge with full power. Mr Gadget and his army attack strongly in return.  

But suddenly, something weird happens. Atriho Boss takes out a gadget and presses the red button on it. Immediately his army’s position changes. They form 1 column such that all 20 members stand one behind the other in a straight line. 

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Atriho presses the red button again and immediately army forms 1 row such that all 20 members stand one beside the other in a horizontal line. The attack continues. 

This continues and soon they shift to 5 and 4 arrangements such that there are five people in each row with four such rows and vice versa. “What is happening? This is so confusing,” says Mr Gadgets over the phone. Uncle Math is confused too. 

But the changing of positions has not stopped! Now the army’s position is 10 people in each row and 2 such rows. Then they shift to 2 people in each row with 10 such rows. “This is getting tougher and tougher! We might lose if this continues,” says Mr Gadgets. 

Everybody is tense now. “Is this some kind of formula that they have been using?” says Squarho. “Why do they divide the army of 20 into groups of 1,2, 4, 5,10, 20! Why not other numbers? Do you have any clue Uncle Math?” says Triho. What do you think is the reason behind this division?

“Because! When you divide 20 with 1, 2, 5,4,10, 20 itself, it leaves no remainder!” says Uncle Math. “Exactly! None of the army members was left behind in any of the arrangements,” says Cirha making connections. “That means Atriho Boss is using Mr Factors,” says Uncle Math. The kids are puzzled. 

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“Mr Factor divides a number using its factors without leaving any remainder. For example, if we take 20 members, I can divide them into groups of 2 and there will be 10 such groups. None of the members will be left here. Similarly, I can reverse the order of arrangement and still none of the members will be left,” explains Uncle Math. 

“The same goes with 5,4,1,20, and 10!” he says. 

“Can I use 3 to divide 20?” asks Squarho. “No! If we divide 20 into groups of 3, there will be 2 members left in the end. Thus 3 is not a factor of 20,” says Triho understanding the whole scenario now. “But,  what do we do now? We need o stop them,” says Cirha. 

“No fear when I am here. We have Mr Reverse Factor,” says Uncle Math. He quickly connects with Mr Gadget and guides him on how to proceed. “All clear!” replies Mr Gadgets. What did Triho tell him? Will they be able to defeat Atriho and his army now?   

Waiting! Waiting! Waiting for the good news. Everybody is tense in Uncle Math’s operating room. 

Suddenly the receiver beeps. Triho rushes to answer it. “As planned, the boot camp is ours! We have successfully defeated Atriho!” says Mr Gadgets. “Hurrah!” Everybody jumps out of joy. But what did Uncle Math actually say that led to their victory?

“Mr Reverse Factor rearranges the number in its original form. That means if 20 was arranged in 5 and 4. It gets back to one line of 20 members again using the gadget,” says Uncle math. “HaHa! Atriho would have had a fun time seeing his gadget not work,” says Squarho. 

Another day of challenges, factors to the rescue and smart use of gadgets! Definitely, a day to remember!

We Learnt That…

  • A factor of a number divides that number without leaving any remainder. 
  • Every number has at least two factors: 1 and itself
  • The easiest way to identify the factors of a number is through the multiplication table.

Let’s Discuss

  • What strategy did Atriho Boss plan for the attack?
  • What was he using to change the positions of the army?
  • What are the factors? How many minimum factors can a number have?
  • How did Uncle Math help us win?

Please refer this guide by Fun2Do Labs for teaching factors and multiples to kids :