Speed up your calculation in bank exam : Number System
Number System
Divisibility Rule:
“Divisible By” means “when you divide one number by another the result is a whole number”Examples:14 is divisible by 7, because 14÷7 = 2 exactly
But 15 is not divisible by 7, because 15÷7 = 2 1/7 (i.e., the result is not a whole number)
“Divisible by” and “can be evenly divided by” mean the same thing
These rules let you test if one number is divisible by another, without having to do too much calculation!
Divisible by  If  Examples 
2  The last digit is even (0,2,4,6,8)  128 is 129 is not 
3  The sum of the digits is divisible by 3 Shortcut : cancel all the 9 and numbers which adding to 9. 
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3)No

4  The last 2 digits are divisible by 4  1312 is (12÷4=3) 7019 is not 
5  The last digit is 0 or 5  175 is 809 is not 
6  The number is divisible by both 2 and 3  114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes 308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No 
7  If you double the last digit and subtract it from the rest of the number and the answer is: 0, ordivisible by 7 
672 (Double 2 is 4, 674=63, and 63÷7=9) Yes
905 (Double 5 is 10, 9010=80, and 80÷7=11 3/7) No

8  The last three digits are divisible by 8 
109816 (816÷8=102) Yes
216302 (302÷8=37 3/4) No

9  The sum of the digits is divisible by 9 Shortcut : cancel all the 9 and numbers which adding to 9. 
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No

10  The number ends in 0  220 is 221 is not 
11  Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc). Then the answer must be:
0, or divisible by 11 
1364 (1−3+6−4 = 0) Yes
913 (9−1+3 = 11) Yes
3729 (3−7+2−9 = −11) Yes
987 (9−8+7 = 8) No

12  The number is divisible by both 3 and 4  648 (By 3? 6+4+8=18 and 18÷3=6 Yes. By 4? 48÷4=12 Yes) Yes 
1)6 — 2 *3 => number should be divisible by 2 and 3 both
2)12—3*4 => number should be divisible by 3 and 4both
3)20—4*5=> number should be divisible by 4 and 5 both
4)30—5*6=> number should be divisible by 5 and 6 both
5)42—6*7=> number should be divisible by 6 and 7 both
6)56—7*8=> number should be divisible by 7 and 8 both
7)72—8*9=> number should be divisible by 8 and 9 both
8)90—9*10=> number should be divisible by 9 and 10 both
Number of prime factor and Total factor
Suppose
T =p^{a}x q^{b}x r^{c} where p ,q ,and r must be prime numbers and a,b,c are the powers of p ,q,and r.
Then ,Total factors = (a+1)(b+1)(c+1).
Total prime factors = (a+b+c).
Remainder concept of few frequently asked model
X ^{even} = what is remainder ? x ^{odd}= what is remainder ?
X+1 x+1
X ^{even} = 1 (when power is even ) x ^{odd}= x (when power is odd)
X+1 x+1
Example :
17^{200} = 1 17^{257} = 17
17+1 17+1
Cyclicity
2^{1}=2  3^{1}=3  4^{1}=4  5^{1}=5  6^{1}=6  7^{1}=7  8^{1}=8  9^{1}=9  
2^{2}=4  3^{2}=9  4^{2}=16  5^{2}=25  6^{2}=36  7^{2}=49  8^{2}=64  9^{2}=81  
2^{3}=8  3^{3}=27  4^{3}=64  5^{3}=125  6^{3}=216  7^{3}=343  8^{3}=512  9^{3}=729  
2^{4}=16  3^{4}=81  4^{4}=256  5^{4}=…….5  6^{4}=1296  7^{4}=2401  8^{4}=4096  9^{4}=….1  
2^{5}=32  3^{5}=243  4^{5}=1024  5^{5}=…….5  6^{5}=7776  7^{5}=…..7  8^{5}=….8  9^{5}=….9  
2^{6}=64  3^{6}=729  4^{6}=4096  5^{6=}……..5  6^{6}=46656  7^{6}=…….9  8^{6}=……4  9^{6}=….1  
2^{7}=128  3^{7}=2187  4^{7}=16384  5^{7}=…….5  6^{7}=2..936  7^{7}=…….3  8^{7}=…….2  9^{7}=….9  
2^{8}=256  3^{8}=6561  4^{8}=65536  5^{8}=……..5  6^{8}= …..6  7^{8}=…….1  8^{8}=……6  9^{8}=….1  
Example : what is unit digit of 4^{23 }= ?
Solution : 4 cyclicity is 2 ,so when we divide 23 by 2 ,we get remainder =1,
Which indicates means 4^{1}=4 , so unit digit of 4^{23} is also will be 4.
So ,friends and students ,today through this article we have seen and learnt some important concept and useful shortcuts tricks which can really speed up your calculation in bank exam.
Must for IBPS aspirants:
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