Chapter 1.
Divisibilty
Read lessons and study through videos.
Divisibilty
Read lessons and study through videos.
Ø Revision :
When one number can be completely divided by another number, ( i.e. without a remainder), then first number is said to be divisible by the second.
For example , 24 can be completely divided by 6, hence, the number 24 is divisible by 6.
Tests for divisibilty by 2, 3, 5 and 10
Test for divisibility by 2 : If a number has any of the digits 0, 2, 4, 6 or 8 in its units place, then that number is divisible by 2.
Test for divisibility by 3 : If the sum of all the digits in a number is divisible by 3, then that number is divisible by 3.
Test for divisibility by 5 : If a number has either 0 or 5 in its units place, then that number is divisible by 5.
Test for divisibility by 10 : If a number has 0 in its units place, then that number is divisible by 10.
Test for divisibility by 4, 6, 9 and 11
Test for divisibility by 4 : If the number formed by the digits in the tens and units places of a number is divisible by 4, then that number also is divisible by 4.
(i) In the number 3148, the number formed by the digits in the tens and units places is 48. This number is divisible by 4. Hence, the number 3148 also is divisible by 4.
(ii) In the number 5019, 19 is not divisible by 4. Verify for yourself that 5019 is not divisible by 4.
Test for divisibility by 6 :
If a number can be divided by the numbers 2 as well as 3, then that number is divisible by 6.
(i) The number 64218 has 8 in the units place. Therefore , it is divisible by 2. The sum of the digits in the number 64218 is 6 + 4 + 2 + 1 + 8 = 21. 21 is divisible by 3. Therefore, 64218 is divisivle by 3. Thus, 64218 is divisible by 2 as well as by 3. Therefore, it is also divisible by 6.
(ii) Verify for yourself that 50918 is not divisible by 6.
Test for divisibility by 9 :
If the sum of the digits in a number is divisible by 9, then that number also is divisible by 9.
(i) The sum of the digits in the number 94,203 is 9+4+2+0+3=18. 18 is divisible by 9. Hence, 94,203 is divisible by 9.
(ii) Verify that 4625 is not divisible by 9 by finding the sum of the digits in the number.
Test for divisibility by 11 : If the difference between the sums obtained by adding alternate digits of the number is 0 or is divisible by 11 then that number, too, is divisible by 11.
(i) The sums of the alternate digits of the number 1452 are 1+5=6 and 4+2=6. The difference between them is 6-6=0. Therefore, 1452 is divisible by 11.
(ii) Take the number 8162. 8+6=14 and 1+2=3. The difference between 14 and 3 is 14-3=11. 11 is divisible by 11. Therefore, 8162 is divisible by 11.
(iii) Verify for yourself that 5123 is not divisible by 11.
FIND MORE TOPICS:
No comments:
Post a Comment