Properties Of Numbers Flashcards
Integer (Definition)
All numbers without a Fractional or Decimal Component inclusive of Positive numbers Negative numbers and zero.
Whole Numbers (Definition)
Set of numbers inclusive of all Non - Negative integers and Zero i.e. Positive numbers without a fractional component and Zero
Integer A is a Multiple of Integer B IF -
A/B = integer i.e A divided B equals to Z which is an Integer
Zero is Multiple of every number!
Since any number divided by zero is zero
i.e it is the only number equal to all its multiples
All numbers are multiples of one A/1 = A
Integer A is a Factor of Integer B IF -
If B/A = integer or B divided A equals to Z which is an Integer
Also, B divided by any factor of A is also equal to an integer.
Zero is not a Factor of any number!
Since division by zero is not allowed
Similarly One is a factor of all Numbers i.e B/1 =B
Square Root of Zero
Is Zero
The only number that is neither positive or Negative
Is Zero
i.e Zero is the only number that is equivalent to its opposite +0 = -0
Zero raised to any number
Is Zero
Note - the exception is Zero raised to Zero which is undefied and not tested
Any number raised to Zero
Is One
Note - the exception is Zero raised to Zero which is undefied and not tested
Zero divided by Any number
Is Zero
I.e. Zero is even since 0/2 is = 0 which is an integer
If (A) (B) = 1
Then A and B are both equal to one or minus one
A number that can be multiplied or divided by any number without changing its value
Is One it is also the only number that is neither Prime nor Composite i.e the smallest prime number is two.
Single-digit Primes
2, 3, 5, 7
10’s Primes
11, 13, 17, 19
20’s Primes
23,29
30’s Primes
31, 37
40’s Primes
41, 43, 47
50’s Primes
53, 59
60’s Primes
61, 67
70’s Primes
71, 73, 79
80’s Primes
83, 89
90’s Primes
97
Find the number of factors of X
Step 1) Prime factorize X such that X = (a^x) (b^y) (c^z)…
where a,b,c are prime numbers and x,y,z are their powers respectively.
Step 2) Add one to each of the exponents and multiply the resulting values i.e (x+1) (y+1) (z+1)…
eg- 240 = (2^4)(3^1)(5^1) i.e factors = (4+1)(1+1)(1+1) = 5x2x2=20
X Divides evenly into Y
Y/X= integer
X is Divisible by Y
X/Y = integer