## Math Story : Divisibility Rules

#### The Divisibility Trick

It is a beautiful morning. All the kids are having fun outside.

“You know what! Give me any number and I will tell you which number from 2 to 10 can completely divide it without leaving any remainder. Come on”, says confident Triho. Everybody bursts into laughter. “Stop kidding”, says Squarho. Nobody is ready to believe Triho.

“You guys don’t believe me? Why don’t you give me a number then and see it yourself?” says Triho. Cirho decides to give it a shot. “Alright! I will give you 34. Which number will divide 34 leaving no remainder?” he says.

“2”, says Triho, without even thinking. He is confident about his answer. Cirho decides to check it on Uncle Math’s gadget. He is surprised by the result. “He is right. Triho is right”, he says. Squarho and Cirha are shocked too.

“34 was a small number. Let me give him a bigger number this time. The number is 357”, says Squarho.

“When 357 is divided by 3, it leaves no remainder”, says Triho confidently. He was super fast again. Others are finding it hard to believe.

Cirha decides to go next. “6500”, she says. “2,5 and 10 can divide 6500 without leaving no remainder”, says Triho again. Can you guess how is he doing this?

Cirho, Cirha and Squarho decide to form a number together and give it to Triho. “Ah! You won’t be able to solve this”, says Squarho overconfidently. “Your number is 29,295”, says Cirha. Do you think Triho could solve this?

Triho starts thinking and doesn’t say the answer initially. “Haha! As we told,  you cannot solve this problem”, laughs Cirho. But suddenly Triho starts smiling. “ 9 is the answer. When 29295 is divided by 9, it leaves no remainder”, he says. Cirha immediately checks the answer and Triho is right again. This is brilliant. But how is Triho doing this?

Everybody is now curious and wants to know the trick behind finding the number that will divide the given number evenly. “How are you doing this? Is it a gadget? Please show us also”, says Squarho.

“Haha! No, it’s not a gadget, it’s a trick. I will teach you the trick”, says Triho.

“In math, a number is said to be divisible by another number if the remainder is 0. There are a certain set of general rules that are often used to determine whether or not a number is evenly divisible by another number. Such rules are called divisibility rules. All we have to do is remember these divisibility rules”, explains Triho.

“I don’t get it. Can you explain with an example?” says Cirha. “Of course. When the last digit of a number is even, the number is divisible by 2”, says Triho. “Oh yes! 34 has 4 in the last digit. 4 is an even number. Thus 34 is divisible by 2”, she says making connections.

“Similarly, to find if a number is divisible by 3 or not, all we have to do is add all the digits of a given number. Then check if the sum is divisible by 3 or not”, explains Triho. “Oh! Just like in 357. When 3,5 and 7 are added, the sum is 15 which is divisible by 3”, says Squarho. Kids are now finding it interesting.

Similarly, Triho explains the divisibility rules of  4,5,6,7,8,9 and 10.

“Wow! This is so easy and fun. Give me a number, and I will try to solve it using the divisibility rule”, says Cirho. “Is 550 divisible by 4?” questions Triho. “The last two digits of 550 are 50. 50 cannot be evenly divided by 4. Thus 550 is not divisible by 4”, says Cirho confidently. Everybody is proud of him.

They continue playing with numbers and testing for divisibility rules. Clearly, a good friend not only teaches you good tricks but also helps you master them.

## We Learnt That…

• There are a certain set of general rules that are often used to determine whether or not a number is evenly divisible by another number. Such rules are called divisibility rules.
• Some of the divisibility rules are:
1. A number that is even or a number whose last digit is an even number i.e. 0, 2, 4, 6, and 8.
2. The sum of all the digits of the number should be divisible by 3.
3. Number formed by the last two digits of the number should be divisible by 4 or should be 00.
4. Numbers having 0 or 5 as their ones place digit.
5. A number that is divisible by both 2 and 3.
6. Number formed by the last 3 digits of the number should be divisible by 8 or should be 000.
7. The sum of all the digits of the number should be divisible by 9.
8. Any number whose one’s place digit is 0.

## Let’s Discuss

• What was Triho boasting about?
• What are divisibility rules?
• Explain the divisibility rules of numbers from 2 to 10 with an example.
• “Clearly, a good friend not only teaches you good tricks but also helps you master them.” Do you agree?