# Mathematics - Class 6 / Grade 6

- Playing With Numbers (Test for Divisibility of Numbers /Divisibility Rules/Divisibility Tests)
### Playing With Numbers (Test for Divisibility of Numbers /Divisibility Rules/Divisibility Tests)

Math - Class 6 - Playing With Numbers (Test for Divisibility of Numbers /Divisibility Rules/Divisibility Tests) - Key Points/Notes/Worksheets/Explanation/Lesson Tags: Tests for Divisibility by 1,2,3,4,5,6,7,8,9,10 and 11 for 6th class, What is the divisibility rule for 7? Finding a number can be divided by 9 for 6th standard, Divisibility Rules of 4 and 8 for grade VI, Practice page on divisibility rules for class VI, Free Worksheet PDF on Test for Divisibility of Numbers for grade 6, Solved Examples of divisibility rule, Determine the divisibility by 11, CBSE Class 6 Math Divisibility of Numbers NCERT Q&A, Question and Solution on divisibility rule, Divisibility Test for 2, Divisibility tests for 2, 3, 4, 5, 6, 9, 10, Worksheets on playing with numbers, Grade 6 Mathematics Playing with Numbers. If a number is divisible by another number then it is divisible by each of the factors of that number. If a number is divisible by two co-prime numbers then it is divisible by their product also. If two given numbers are divisible by a number, then their sum is also divisible by that number. If two given numbers are divisible by a number; then their difference is also divisible by that number.### Tests for Divisibility of Numbers

Is the number 27 divisible by 2? by3? by4?

By actually dividing 27 by these numbers we find that it is divisible by 3 but not by 2 and by 4. A number is exactly divisible by another number, when quotient is a whole number and the resulting remainder is zero.

Sometimes actual division of huge number can be very tedious. We can test if one number is divisible by another, without doing too much calculation using divisibility rules. By using divisibility rules, we can find out whether one number is divisible by another number just by examining the digits of the number. It is a quick way to find factors of large numbers.

### Divisibility Rules

These below rules will help us to know whether one number is divisible by another without much calculation.

__Divisibility by 1__Any integer (not a fraction) is divisible by 1.Divisibility rule for 1 doesn’t have any particular condition. Any number divided by 1 will give the number itself, irrespective of how large the number is.

Example:

15 ÷ 1, Quotient=15, Remainder=0

9999 ÷ 1, Quotient=9999, Remainder=0

__Divisibility by 2__A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.

Example:

Is 3110, 2222, 5974, 4356 and 1468 divisible by 2?

Numbers 311

**0**, 222**2**, 597**4**, 435**6**and 146**8**are divisible by 2 as these numbers have only the digits**0**,**2**,**4**,**6**,**8**in the ones place.__Divisibility by 3__If the sum of the digits of the given number is divisible by 3, then the given number is also divisible by 3.

Example 1:

Is 7221 divisible by 3?

Sum of the digits of 7221 = 7 + 2+ 2 + 1 = 12

Number ‘12’ is divisible by 3 (12 ÷ 3 = 4). So, 7221 is also divisible by 3.

Example 2:

Find the smallest digit and the greatest digit in the blank space of the number so that the number formed is divisible by 3.

_6724

Sum of the digits = * + 6 + 7 + 2 + 4 = * + 19

To make the number divisible by 3, sum of its digits should be divisible by 3.

The smallest multiple of 3 that comes after 19 is 21.

Therefore, the smallest number is 21-19 = 2.

Now, 2+3+3 = 8 (no more 3 can be added as it will become two digits)

If we place 8, then the sums of the digits will be 27 and as 27 is divisible by 3, the given number will also be divisible by 3.

__Divisibility by 4__A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

Example:

Is 46

**24**divisible by 4?The last two digit of the given number is

**24**.**24**÷ 4 = 6 (**24**is divisible by 4)So, 14624 is divisible by 4

__Divisibility by 5__A number which has either 0 or 5 in its ones place is divisible by 5.

Example:

Is 510

**5**divisible by 5?Here last digit is

**5**. So, 5105 is divisible by 5.__Divisibility by 6__If a number is divisible by 2 and 3 both then it is divisible by 6 also.

Example:

Is 433

**5**divisible by 6?**Step 1**: Test of divisibility by 2.Number 4335 end in odd number (i.e.

**5**). So, 4335 is not divisible by 2.**Step 2**: Test of divisibility by 3.Sum of the digit of the given number 4335 = 4 + 3 + 3 + 5 = 15

Number ‘15’ is divisible by 3. So, 4335 is divisible by 3.

Given number 4335 is divisible by 3 but not by 2. So, 4335 is not divisible by 6.

__Divisibility by 7__Double the last number of the given number and then subtract it from the rest of the number left in the given number. If the answer we get is either 0 or any number divisible by 7, then the given number is divisible by 7.

Example:

Is 449

**4**divisible by 7?**Step1:**Double the last digitHere last digit is

**4**. Double of**4**is 8.**Step2:**Subtract the answer from the rest of the number.Number left is 449. So, subtract 8 from 449.

449 – 8 = 441

**Step3:**Number 441 is divisible by 7. So, 4494 is divisible by 7__Divisibility by 8__A number is divisible by 8, if the number formed by its last three digits is also divisible by 8.

Example:

Is the number 73

**512**divisible by 8?Here last three digits are

**512**.**512**÷ 8 = 64As

**512**is completely divisible by 8. So, the given 73512 is also divisible by 8.__Divisibility by 9__Given number is divisible by 9, if the sum of the all the digits of given number is divisible by 9.

Example:

Is 6687 divisible by 9?

Sum of the digit = 6 + 6 + 8 + 7 = 27

Number ‘27’ is divisible by 9. So, the given number 6687 is divisible by 9.

__Divisibility by 10__Any number that ends in 0 is divisible by 10.

Example:

Is 367

**0**divisible by 10?As number ends in

**0**.So, 3670 is divisible by 10.__Divisibility by 11__Starting from left add all the number on odd positions and add all the number on even positions. Then subtract the two results. If the resultant number is divisible by 11 or is equal to 0, then the given number is divisible by 11.

Example:

Is

**3**7**2**9 divisible by 11?Sum of odd positions =

**3**+**2**=**5**Sum of even positions = 7 + 9 = 16

Subtract the two results, 16 –

**5**= 11. As the resultant number 11 is divisible by 11, so 3729 is divisible by 11.**Some More Divisibility Rules**#### 1. If a number is divisible by another number then it is divisible by each of the factors of that number.

Example:

Is 1488 divisible 12?

1488 ÷ 12 = 124

Yes, 1488 is divisible by 12. Therefore, number 1488 is also divisible by factors of 12 (i.e. 1, 2, 3, 4, 6 and 12).

#### 2. If a number is divisible by two co-prime numbers then it is divisible by their product also.

Example:

1365 ÷ 3 = 455

1365 ÷ 5 = 273

Here, divisor 3 and 5 are

__co-prime__numbers. Therefore, given number 1365 is also divisible by the__product__of 3 and 5.1365 ÷ 15 (3x5=15) = 91

#### 3. If two given numbers are divisible by a number, then their sum is also divisible by that number.

Example:

245 ÷ 5 = 49

405 ÷ 5 = 81

The numbers 245 and 405 are both divisible by 5. Therefore,

__sum__of 245 and 405 is also divisible by 5.650 ÷ 5 = 130 (Note: 245 + 405 = 650)

#### 4. If two given numbers are divisible by a number; then their difference is also divisible by that number.

Example:

1722 ÷ 7 = 246

875 ÷ 7 = 125

The numbers 1722 and 875 are both divisible by 7. Therefore,

__difference__of 1722 and 875 is also divisible by 7.847 ÷ 7 = 121 (Note: 1722 - 875 = 847)

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