Question

Write the divisibility Rule of number 2, 3, 5, 6 , 9 and 11 . Explain 2 example each

Answer 1

Step-by-step explanation:

Given :-

2,3,5,6,9,11

To find :-

Write the divisibility rules of the given numbers ?

Solution :-

Divisibility by 2:-

A number is divisible by 2, if the number has one of the digits 2,4,6,8,0 in its ones place.

Ex:-

1)256890 is divisible by 2 ,because 0 is in its ones place.

2) 1200008 is divisible by 2 , because 8 is in its ones place

Note :-

• The multiples of 2 are also divisible by 2
• Even numbers are also divisible by 2

Divisibility by 3:-

If the sum of the digits is divisible by 3 then the number is divisible by 3.

Ex:-

1) 2562 is divisible by 3 because the sum of the digits = 2+5+6+2 = 15 is divisible by 3.

2) 10008 is divisible by 3 because the sum of the digits 1+0+0+0+8 = 9 is divisible by 3.

Note :-

• Multiples of 3 are also divisible by 3

Divisibility by 5:-

The number is divisible by 5 ,if it has either 0 and 5 in its ones place.

Ex:-

1) 250000 is divisible by 5 ,because 0 is in its ones place.

2) 235866665 is divisible by 5 ,because 5 is in its ones place.

Note :-

• Multiples of 5 are divisible by 5

Divisibility by 6 :-

If a number is divisible by both 2 and 3 then it is divisible by 6.

Ex:-

1) 552 is divisible by 6 because it is divisible by both 2 and 3

2 is in its ones place so, it is divisible by 2

The sum of digits = 5+5+2 = 12 is divisible by 3

2) 108 is divisible by 6 because it is divisible by both 2 and 3.

8 is in its ones place so it is divisible by 2

Sum of the digits = 1+0+8 = 9 is divisible by 3

Note :-

• Multiples of 6 are divisible by 6.

Divisibility by 9:-

If the sum of the digits is divisible by 9 then the number is divisible by 9

Ex:-

1) 25623 is divisible by 9 because the sum of the digits = 2+5+6+2+3= 18 is divisible by 9.

2) 10008 is divisible by 9 because the sum of the digits 1+0+0+0+8 = 9 is divisible by 9

Note :-

• Multiples of 9 are also divisible by 9

Divisibility by 11:-

The difference between the sum of the digits at even places and the sum of the digits at odd places in a number is either 0 or multiple of 11 ,the number is divisible by 11.

Ex:-

1) 1001 is divisible by 11 because

The sum of the digits at even places = 0+1 = 1

The sum of the digits at odd places = 1+0 = 1

Their difference = 1-1 = 0

So it is divisible by 11.

2) 8151 is divisible by 11 because

The sum of the digits at even places = 1+1= 2

The sum of the digits at odd places = 5+8 = 13

Their difference = 13-2 = 11

So it is divisible by 11.

Note :-

• Multiples of 11 are divisible by 11.