The Secret Code

Topic: Prime Factorization Using Factor Tree Method

“Uncle Bad has not learnt his lesson yet. He is planning to steal our advanced gadgets from the secret locker. We have to do something”, says Uncle Science on the call. Uncle Math is worried. What will they do now?

“Triho, I need your help!” says Uncle Math and explains everything to him. Triho listens calmly and thinks of various solutions. 

“Idea! How about we have a secret password that cannot be decoded by anyone?” suggests Triho. “Oh yes! This is a brilliant idea. But what should be the password?” thinks Uncle Math. Can you think of a secret code that cannot be decoded easily?

Suddenly, Uncle Math starts smiling. It looks like he has figured out something. “Come on, follow me”, he says. Triho immediately runs behind him. 

Uncle Math types something on the secret locker. What is he upto? Is he changing the password of it?

“Alright! I have reset the password of the secret locker. It is 24. Triho, can you type it and unlock the locker?” instructs Uncle Math. Triho does as said. “2.. 4! Enter”, he says. But the locker does not get unlocked. He is confused.

He decides to try again. “2….4! Enter”, the locker does not open again. “What is this Uncle Math? I think there is some problem with the locker”, he says. Uncle Math bursts into laughter.  “Haha! There is nothing wrong with it. I’ll show you”, says Uncle Math. 

He enters 2 first, then 2, then 2 and finally 3. Beep! The secret locker unlocks immediately. “Whoa!  2,2,2 and 3 are not 24. How did you unlock the locker this way?” he wonders. “Do not worry, I will explain everything”, says Uncle Math and starts writing on the board. 

“2,2,2 and 3 are the prime factors of 24. When we express a number as a product of its prime factors, is called prime factorization”, explains Unce Math. “Prime factors? What are they?” says confused Triho.   

“A factor that is a prime number is called a prime factor. A number which has only 1 and itself as factors are called a prime number. In the case of 24, 2 and 3 are prime numbers as they have only 1 and itself their factors. So here we express 24 as a product of its prime factors. Multiplying 2x2x2x3 gives us 24”, explains Uncle Math. 

“This is amazing! So you have set the locker to accept only prime factors as inputs. This is the best secret language. But how do I find the prime factors?” asks Triho. “It is very simple. I’ll show you a method”, says Uncle Math. 

Uncle Math writes 24 in a circle and draws two more circles as its branches. “Can you tell me two numbers whose product is 24?” asks Uncle Math. “6 and 4”, says Triho. Uncle Math fills the circle with the same. 

“Can I further write the  6 and 4 in products?” he asks. “Oh yes! Multiplying 2 and 3 gives us 6. Multiplying 2 and 2 gives us 4”, says Triho. Uncle Math writes the same. 

“Look at the numbers carefully, can we further write them as a product of two numbers without multiplying the number itself with 1?” asks Uncle Math. Triho observes carefully and says,” 2×1 will give 2. 3×1 will give 3. So the answer is no.”

“Exactly. You have arrived at the prime factors of the number”, says Uncle Math with a smile. Triho understands everything now. “This is so simple. All I have to do is keep expressing the number as a product of its factors until I reach the prime numbers”, he says. Uncle Math agrees. 

Triho decides to reset the password to 48 this time. What code would you use to unlock the secret locker? 

2x2x2x2x3 will give us 48. Uncle Math enters the same digits. Beep! The secret locker opens. Both of them are happy. 

Suddenly they hear a sound. “Looks like Uncle Bad is here. Let’s quickly lock the secret locker and hide”, says Uncle Math. 

But before they could hide, Uncle bad finds them and orders his army to catch them. “Haha! 48 ah. So silly. I will take all these gadgets to destroy the galaxy using these. This is amazing. Uncle Math, you are over”, he says and tries to open the locker. But the locker does not open. 

Surprised, he tries many ways but nothing works. Furiously, he asks, “What is the password?” Uncle Math and Triho do not reveal anything. He gets even more frustrated. 

“Haha! You consider yourself really smart right? Then why can’t you open the secret locker? Does this prove that you are a loser?” provokes Uncle Math. Uncle Bad loses his calm and starts attacking both of them. 

Both Uncle Math and Triho fight him bravely. But Uncle Bad uses his powerful laser gun and attacks Uncle Math. He immediately faints. Triho rushes to see him. 

“What if I could not get the gadgets, I have done enough harm to your Uncle Math. Haha! I am Uncle Bad. I make everyone sad”, he says and leaves with his army. 

Triho immediately calls Uncle Science and seeks his help. Uncle Science uses his medicines and soon, Uncle Math gains consciousness. “My secret locker! Are my gadgets safe?” he asks immediately. 

“Yes, the gadgets are safe. Your prime factorization technique saved the gadgets from Uncle Bad. You are a genius Uncle Math”, praises Triho. Uncle Math sighs in relief. A secret locker, an interesting code, a brave fight and gadgets being saved. It was an adventurous day indeed.

We Learnt That…

  • A number which has only 1 and itself as factors are called prime numbers.
  • A factor that is a prime number is called a prime factor.
  • When we express a number as a product of its prime factors, is called prime factorization.
  • Factor tree method is one of the methods to find prime factors of a number.

Let’s Discuss

  • Why was Uncle Math worried?
  • How did Uncle Math decide to set the password?
  • What is a prime number? What is a prime factor?
  • What is prime factorization? Explain with an example.