05.07 वैदिक गणित (07) || भाग || 15 की विभाज्यता के नियम

05.07 वैदिक गणित (07) || भाग || 15 की विभाज्यता के नियम 

लेखक

ॐ जितेन्द्र सिंह तोमर

M.A., B.Ed., DNYS, MASSCOM

10/7/28/11/2021

05.07 वैदिक गणित (07) || भाग || 15 की विभाज्यता के नियम 

Division:

DIVISIBILITY BY 15

Divisibility by 15

Any number will be divisible by 15 if it is divisible by 5 and by 3 both. 

So the test for both 5 and 3 is must to pass for divisiblty of 15.

All numbers divisible by both 3 and 5 are divisible by 15

345 is divisible by 5, but also by 3 (as its digit sum is 3) so 345 is divisible by 15.

Exercise 01

Find which of the following are divisible for not by 15.

01) 12645

02) 54867

03) 35212

04) 60683

05) 840256

06) 770878

07) 100497

08) 7552567

09) 2120102

10) 1248273

11) 13500056

12) 31085675

13) 14224086

14) 413541657

15) 265435263

16) 614650058

17) 5872625667

18) 85912672546

19) 12852456645

20) 21570364865

21) 751283251265

22) 123456080843

23) 123456728884

24) 1234567548006

25) 1234567890648

Sol. 01) 

Test 01.

The digital sum of the number 12645 is 1+2+6+4+5= 18 = 1+8=9, so that 12645 is divisible by 3

Test 02.

The unit digit of 12645 is 5 so that this is divisible by 2. 

Conclusion

* Thus it pass the test for both 3 and 5 both so that the numbers 12645 will be divisible by 15. 

Sol. 21) 

Test 01.

The digital sum of the number 13500056 is 1+3+5+0+0+0+5+6 = 2+0=2, so that 13500056 is not divisible by 3

Test 02.

The unit digit of 13500056 is 6 so that this is not divisible by 5. 

Conclusion

* Thus it does not pass the test for 3 and 5 both so that the numbers 13500056 will not be divisible by 15. 

Sol. 21) 

Test 01.

The digital sum of the number 751283261265 is 7+5+1+2+8+3 + 2+ 6+1+2+6+5 = 4+8=1+2=3, so that 751283261265 is divisible by 3

Test 02.

The unit digit of 751283261265 is 5 so that this is divisible by 5. 

Conclusion

* Thus it pass the test for 3 and 5 both so that the numbers 751283261265 will be divisible by 15. 

MIND IT 

Divisibility Tests: Summary

Number tested => Test

0,2 => If the last digit 0 or even.

3,6,9 => If the digit Sum 3, 6 or 9.

4 => If the last 2 digit of number are divisible by 4.

5 => If the last digit is 0 or 5.

6 => If the number is divisible by both 2 and 3.

8 => If the last 3 digit of number are divisible by 8.

9 => If the digit sum is 9

10 => Is the last digit 0.

15 => Is the number divisible by both 3 and 5.