Number System
BODMAS' Rule
'B' stands for 'Bracket', 'O' for 'of', 'D' for 'Division', 'M' for 'Multiplication', 'A' for 'Addition' and 'S' for 'Subtraction'
Dividend =
(Divisor × Quotient) + Remainder
(x∧n - a∧n) is divisible by
(x + a) for all even values of n.
(x∧n + a∧n) is divisible by
(x + a) for all odd values of n.
(x∧n - a∧n) is divisible by
(x - a) for all values of n.
Integers
- 3, - 2, - 1, 0, 1, 2, 3, ........... are all integers. Set of positive integers = {1, 2, 3, 4, 5, 6, ...........} Set of negative integers = { - 1, - 2, - 3, - 4, - 5, - 6, ...........} Set of all non-negative integers = {0, 1, 2, 3, 4, 5, ...........}
0 / anything
0
Whole Numbers
0, 1, 2, 3, 4, ........... are all whole numbers
0⁰
1
anything⁰
1
Natural Numbers
1, 2, 3, 4, ........... are all natural numbers.
Divisibility By 7 or 13:
1. Divide number into groups of 3 digits (starting from right) 2. find the difference between the sum of the numbers in odd and even places. 3. If the difference is 0 or divisibleby 7 or 13 (as the case may be), it is divisible by 7 or 13.
Divisibility of 8
1. divisible by 2 three times 2. Last 3 digits divisible by 8
Test of prime number
1. nearest square root of number 2. divide the number by all prime numbers lower than square root number 3. if not divisible any is prime
only even prime number
2
smallest prime number
2.
first odd prime number
3
Approximation
3572 124 514.6826 3 - billion 5 - hundred million 7 - Ten million/Crores 2 - Million/Ten Lakhs 1 - Hundred Thousand/Lakhs 2 - Ten thousands 4 - Thousands 5 - Hundred 1 - Ten 4 - Ones 6 - Tenths 8 - Hundredths 2 - Thousandths 6 - Ten thousandths
least composite number
4
101 to 200 prime numbers
411 31 222 14 101, 103, 107, 109 113 127 131, 137, 139 149 151, 157 163, 167 173, 179 181 191, 193, 197, 199
1 to 100 prime numbers
44 22 322 321 2, 3,5, 7 11, 13, 17, 19 23, 29 31, 37 41, 43, 47 53, 59 61, 67 71, 73, 79 83, 89 97
6872 the face value of 7
7
70984 Place value of 8
80
least odd composite number
9.
Divisibility of 4
Divisible by 2 or Last two digits divisible by 4
Divisibility of 6
Divisible by both 2 & 3
Even / Odd
Even
Even∧Even
Even
Even∧Odd
Even
Even number + Even number =
Even number
Even number - Even number =
Even number
Even number × Even number =
Even number
Even number × Odd number =
Even number
Odd number + Odd number =
Even number
Odd number - Odd number =
Even number
Even / Even
Even or Odd
Odd / Even
Fraction
HCF of fraction
HCF of numerator/ LCM of denominator
product of numbers =
LCM * HCF
LCM of fraction
LCM of numerator/ HCF of denominator
0 / 0 or anything / 0
Not defined
Odd / Odd
Odd
Odd∧Even
Odd
Odd∧Odd
Odd
Even number + Odd number =
Odd number
Even number - Odd number =
Odd number
Odd number - Even number =
Odd number
Odd number × Odd number =
Odd number
Multiplication of a Number By 5∧n
Put n zeros to the right of the multiplicand and divide the number so formed by 2∧n.
Co-primes (or Relative Primes)
Two numbers whose H.C.F. is 1 are called co-prime numbers (2, 3), (8, 9)
Twin Primes
Two prime numbers whose difference is 2 (3, 5), (5, 7), (11, 13)
0 is
a whole number which is not a natural number
Divisibility of 11
difference between the sum of its digit at odd places and sum of digit at even places is either 0 or a number divisible by 11
Divisibility of 5
ends in 0 or 5
Divisibility of 2
even or zero
Prime Numbers:
exactly two factors
Divisibility By 16
last 4 digits is divisible by 16
Divisibility By 25
last two digits is either 00 or divisible by 25
Composite Numbers:
more than 2 factors
1
neither prime nor composite
All whole numbers are
not natural numbers
Rational Numbers
p/q
H.C.F can be
positive not negative
Divisibility of 3
sum of integers digit divisible by 3
Divisibility of 9
sum of integers divisible by 9
Divisibility of 7
take last digit > double it > subtract doubled no from the main no > result is divisible by 7
divisor of a number can't be more than
that integer
Perfect Numbers:
the sum of whose factors (except the number itself), is equal to the number factors of 6 are 1, 2, 3 and 6. And, 1 + 2 + 3 = 6.
All natural numbers are
whole numbers.
Irrational Numbers:
√2,√3, √5, √7 , , , 0.231764735...... π e
