Question

1. Write the divisibility rules of numbers 2, 3, 5, 6, 9 and 11. Explain with 2 examples each.

Answer 1

Answer:

Divisibility rule of 2

A number is divisible by 2 if the digit in the unit place is 2,4,6,8,0

Examples:

1. 87356: In this number, the digit in the unit place is 6, hence the number is divisible by 2
2. 347921:  In this number, the digit in the unit place is 1, hence the number is not divisible by 2

Divisibility rule of 3

A number is divisible by 3 if the sum of digits of the number is divisible by '3'

Examples:

1. 87356: Here, 8+7+3+5+6 =29, Since 29 is not divisible by 3, 87356 is not divisible by 3.
2. 347931: Here, 3 +4 +7 +9 +3 +1 = 27, Since 27 is divisible by 3, 347931 is divisible by 3

Divisibility rule of 5

A number is divisible by 5 if the digit in the unit place is either 5 or 0

Examples:

1. 87355: In this number, the digit in the unit place is 5, hence the number is divisible by 5
2. 347921:  In this number, the digit in the unit place is 1, hence the number is not divisible by 5

Divisibility rule of 6

A number is divisible by 6 if it is divisible by 2 and 3

Examples:

1. 87354:  In this number, the digit in the unit place is 4, hence the number is divisible by 2. Also, 8+7+3+5+4 =27, Since 27 is divisible by 3, 87354 is divisible by 3. Since 87354 is divisible by both 2 and 3, it is divisible by 6
2. 347931: In this number, the digit in the unit place is 1, hence the number is not divisible by 2. Since it is not divisible by 2, it is not divisible by 6

Divisibility rule of 9

A number is divisible by 9 if the sum of digits of the number is divisible by '9'

Examples:

1. 87356: Here, 8+7+3+5+6 =29, Since 29 is not divisible by 9, 87356 is not divisible by 9.
2. 347931: Here, 3 +4 +7 +9 +3 +1 = 27, Since 27 is divisible by 9, 347931 is divisible by 9

Divisibility rule of 11

A number is divisible by 11 if the alternate sum of digits of the number taken from left to right is divisible by '11'

Examples:

1. 87356: Here, 8-7+3-5+6 = 5, Since 5 is not divisible by 11, 87356 is not divisible by 11.
2. 3479311: Here, 3 -4 +7 -9 +3+1 -1 = , Since 0 is divisible by 11, 3479311 1is divisible by 11

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