Maharashtra Board Class 6 Maths part 1 Chapter 8 Divisibility PDF Download

Divisibility

Let's Recall

Write the divisibility tests for 2, 5 and 10.

Read the numbers given below. Which of these numbers are divisible by 2, by 5 or by 10? Write them in the empty boxes.

125, 364, 475, 750, 800, 628, 206, 508, 7009, 5345, 8710

Teacher's Note

When we check if a number is divisible by 2, we only look at the last number. If it is even, like 4, 6, 8, or 0, then the whole number is divisible by 2. Just like in shops, we divide money into 2 equal parts.

Exam Trick

Remember: If the last digit is even (0, 2, 4, 6, 8), the number is divisible by 2. If the last digit is 0 or 5, the number is divisible by 5. If the last digit is 0, the number is divisible by both 5 and 10.

Points to Remember

A number is divisible by 2 if its last digit is even.
A number is divisible by 5 if its last digit is 0 or 5.
A number is divisible by 10 if its last digit is 0.
We do not need to divide to check divisibility.

Let's Learn

Divisibility Tests

Let us study some more tests.

Complete the table below.

What can we conclude from this?

Divisibility test for 3: If the sum of the digits in a number is divisible by 3, then the number is divisible by 3.

Teacher's Note

To check if a number is divisible by 3, add all the digits. If the answer is divisible by 3, then the whole number is divisible by 3. For example, 27 has digits 2 + 7 = 9, and 9 is divisible by 3, so 27 is divisible by 3.

Exam Trick

Remember: Add all digits. If the sum is divisible by 3, the number is divisible by 3. You do not need to divide the big number by 3. Just add the digits and check the sum.

Points to Remember

Add all the digits in the number.
Check if the sum is divisible by 3.
If yes, the whole number is divisible by 3.
If no, the whole number is not divisible by 3.

Complete the following table.

What can we conclude from this?

Divisibility test for 4: If the number formed by the digits in the tens and units places of the number is divisible by 4, then that number is divisible by 4.

Teacher's Note

To check if a number is divisible by 4, only look at the last two digits. If those two digits form a number divisible by 4, then the whole number is divisible by 4. For example, in 516, the last two digits are 16, and 16 is divisible by 4, so 516 is divisible by 4.

Exam Trick

Remember: Only look at the last two digits. Do not check the whole number. If the last two digits are divisible by 4, the whole number is divisible by 4.

Points to Remember

Look only at the last two digits of the number.
Check if those two digits are divisible by 4.
If yes, the whole number is divisible by 4.
If no, the whole number is not divisible by 4.

Complete the following table.

What can we conclude from this?

Divisibility test for 9: If the sum of the digits of a number is completely divisible by 9, then the number is divisible by 9.

Teacher's Note

To check if a number is divisible by 9, add all the digits. If the sum is divisible by 9, then the whole number is divisible by 9. For example, 81 has digits 8 + 1 = 9, and 9 is divisible by 9, so 81 is divisible by 9.

Exam Trick

Remember: Add all digits. If the sum is divisible by 9, the number is divisible by 9. Divisibility test for 9 is just like divisibility test for 3, but we check if the sum is divisible by 9.

Points to Remember

Add all the digits in the number.
Check if the sum is divisible by 9.
If yes, the whole number is divisible by 9.
If no, the whole number is not divisible by 9.
The sum of digits must divide exactly by 9.

Practice Set 22

There are some flowering trees in a garden. Each tree bears many flowers with the same number printed on it. Three children took a basket each to pick flowers. Each basket has one of the numbers, 3, 4 or 9 on it. Each child picks those flowers which have numbers divisible by the number on his or her basket. He or She takes only 1 flower from each tree. Can you tell which numbers the flowers in each basket will have?

Numbers on flowers: 111, 220, 249, 999, 432, 336, 666, 450, 369, 435, 356, 960, 72, 123, 108, 90

Teacher's Note

In this activity, children learn to use divisibility tests in a fun way. They pick flowers with numbers that are divisible by their basket number. This is like sorting items in a real shop where we group things by type.

Exam Trick

Remember: Use the divisibility test for 3 (add digits), test for 4 (check last two digits), and test for 9 (add digits). Do not divide the number. Just use the tests to check quickly.

Points to Remember

For basket 3, use divisibility test for 3.
For basket 4, use divisibility test for 4.
For basket 9, use divisibility test for 9.
One flower can go into only one basket.
Check all numbers and sort them correctly.

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