लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM
10/7/28/11/2021
05.02 वैदिक गणित (02) || भाग || 2, 5 व 10 की विभाज्यता के नियम
Division:
DIVISIBILITY BY 2
By Viloknam Method
Look at the following Series 1, 3, 5, 7, 9, 11, 13, 15, 17, ......
All numbers ending in odd numbers like 1, 3, 5, 7, 9 are not divisible by 2.
Whenever
We Look at the following Series 2, 4, 6, 8, 10, 12, 14, 16, ......
All numbers ending in even numbers like 2, 4, 6, 8 With zero and have 2 as a factor so that these are divisible by 2.
* We can say that all numbers ending in even numbers or zero are divisible by 2 but ending in odd numbers are not divisible by 2
Any number ending in 0, 2, 4, 6 and 8 is divisible by 2.
Or
Any number with unit digit 0 or 2 or 4 or 6 or 8 is divisible by 2.
Exercise 01
Find which of the following are divisible for not by 2.
01) 2
02) 4
03) 3
04) 6
05) 8
06) 7
07) 10
08) 19
09) 21
10) 12
11) 13
12) 31
13) 14
14) 41
15) 26
16) 60
17) 58
18) 85
19) 120
20) 2157
21) 75128
22) 123456
23) 1234567
24) 12345678
25) 1234567890
Sol.
01) 2 is its unit so it is divisible by 2.
03) 3 is its unit and is not even or zero so that it is not divisible by 2.
07) Unit digit of 10 is 0 so that it is divisible by 2.
08) Unit digit of 19 is 9 so that it is not divisible by 2.
09) Unit digit of 120 is 0 so that it is divisible by 2.
20) Unit digit of 2157 is 7 so that it is not divisible by 2.
25) Unit digit of 1234567890 is 0 so that it is divisible by 2.
DIVISIBILITY BY 5
By Viloknam Method
Look at the following Series 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ......
All numbers ending in 5 or zero are divisible by 5.
* We can say that
Any number ending in 0 and 5 is divisible by 5, otherwise not.
or
Any number with unit digit 0 or 5 is divisible by 5, otherwise not.
Exercise 02
Find which of the following are divisible for not by 5.
01) 27
02) 54
03) 35
04) 60
05) 84
06) 77
07) 10
08) 75
09) 211
10) 124
11) 135
12) 310
13) 142
14) 413
15) 265
16) 600
17) 587
18) 859
19) 1205
20) 21570
21) 751283
22) 123456
23) 1234567
24) 12345675
25) 1234567890
Sol.
01) Unit digit of 27 is 7 so that it is not divisible by 5.
03) Unit digit of 35 is 5 so that it is divisible by 5.
07) Unit digit of 211 is 1 so that it is not divisible by 5.
08) Unit digit of 19 is 9 so that it is not divisible by 2.
19) Unit digit of 1205 is 5 so that it is divisible by 5.
25) Unit digit of 1234567890 is 0 so that it is divisible by 5.
DIVISIBILITY BY 10
By Viloknam Method
Look at the following Series 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, ......
All numbers ending in zero are divisible by 10.
* We can say that
Any number ending in 0 is divisible by 10, otherwise not.
or
Any number with unit digit 0 is divisible by 10, otherwise not.
Exercise 03
Find which of the following are divisible for not by 10.
01) 20
02) 54
03) 35
04) 60
05) 84
06) 77
07) 10
08) 750
09) 211
10) 124
11) 135
12) 310
13) 142
14) 413
15) 265
16) 600
17) 587
18) 859
19) 1205
20) 21570
21) 751283
22) 123450
23) 1234567
24) 12345675
25) 1234567890
Sol.
01) Unit digit of 20 is 0 so that it is divisible by 10.
03) Unit digit of 35 is 5 so that it is not divisible by 10.
07) Unit digit of 211 is 1 so that it is not divisible by 10.
08) Unit digit of 750 is 0 so that it is divisible by 10.
19) Unit digit of 1205 is 5 so that it is not divisible by 10.
25) Unit digit of 1234567890 is 0 so that it is divisible by 10.
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