Test for Divisibility of a number in traditional methods
>> Monday, June 29, 2009
Introduction:
In traditional methods, we are taught about checking divisibility by numbers like 2, 3, 4, 5, 6, 8, 9, 10 and 11. We will see the divisibility rule for each of the numbers one by one.
Divisibility test by 2:
A number is divisible by 2 if its last digit is divisible by 2.
Means if the last digit of a number is 0, 2, 4, 6, or 8, then it is divisible by 2.
Example: 12, 76, 1546694 are divisible by 2
5, 87, 6865459 are not divisible by 2
Divisibility test by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 3.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 3.
Divisibility test by 4:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Example: 124 is divisible by 4 as 24(last two digits of 124) is divisible by 4.
12780 is divisible by 4 as 80 is divisible by 4.
962 is not divisible by 4 as 62 is not divisible by 4.
Divisibility test by 5:
A number is divisible by 5 if its last digit is 0 or 5.
Example: 1265 is divisible by 5
230 is divisible by 5
567 is not divisible by 5
Divisibility test by 6:
A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 432 is divisible by 6 as it is divisible by both 2 and 3.
1439 is not divisible by 6.
Divisibility test by 8:
A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.
Example: 12108 is divisible by 8
54800 is divisible by 8
Divisibility test by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.
Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 9.
34587: 3 + 4 + 5 + 8 + 7=27 and 27: 2 + 7 = 9. So, 34587 is divisible by 9.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 9.
Divisibility test by 10:
A number is divisible by 10 if its last digit is 0.
Example: 12650 is divisible by 10
Divisibility test by 11:
Find x = sum of odd numbered digits and y = sum of even numbered digits.
If (x-y) is 0 or multiple of 11, then the number is divisible by 11.
Example:
(1) 121: x = 1 + 1 =2
y = 2
x-y = 0
Hence, 121 is divisible by 11.
(2) 879197: x = 8 + 9 + 9 = 26
y = 7 + 1 + 7 =15
x – y = 26 – 15 = 11
Hence, 879197 is divisible by 11.
I will post content for divisibility test by prime numbers like 7, 13, 17, 23 etc which are not taught in our school sylabus.
Regards,
Banshi.
In traditional methods, we are taught about checking divisibility by numbers like 2, 3, 4, 5, 6, 8, 9, 10 and 11. We will see the divisibility rule for each of the numbers one by one.
Divisibility test by 2:
A number is divisible by 2 if its last digit is divisible by 2.
Means if the last digit of a number is 0, 2, 4, 6, or 8, then it is divisible by 2.
Example: 12, 76, 1546694 are divisible by 2
5, 87, 6865459 are not divisible by 2
Divisibility test by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 3.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 3.
Divisibility test by 4:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Example: 124 is divisible by 4 as 24(last two digits of 124) is divisible by 4.
12780 is divisible by 4 as 80 is divisible by 4.
962 is not divisible by 4 as 62 is not divisible by 4.
Divisibility test by 5:
A number is divisible by 5 if its last digit is 0 or 5.
Example: 1265 is divisible by 5
230 is divisible by 5
567 is not divisible by 5
Divisibility test by 6:
A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 432 is divisible by 6 as it is divisible by both 2 and 3.
1439 is not divisible by 6.
Divisibility test by 8:
A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.
Example: 12108 is divisible by 8
54800 is divisible by 8
Divisibility test by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.
Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 9.
34587: 3 + 4 + 5 + 8 + 7=27 and 27: 2 + 7 = 9. So, 34587 is divisible by 9.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 9.
Divisibility test by 10:
A number is divisible by 10 if its last digit is 0.
Example: 12650 is divisible by 10
Divisibility test by 11:
Find x = sum of odd numbered digits and y = sum of even numbered digits.
If (x-y) is 0 or multiple of 11, then the number is divisible by 11.
Example:
(1) 121: x = 1 + 1 =2
y = 2
x-y = 0
Hence, 121 is divisible by 11.
(2) 879197: x = 8 + 9 + 9 = 26
y = 7 + 1 + 7 =15
x – y = 26 – 15 = 11
Hence, 879197 is divisible by 11.
I will post content for divisibility test by prime numbers like 7, 13, 17, 23 etc which are not taught in our school sylabus.
Regards,
Banshi.
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