. math

• Whole (natural) numbers


  Numbers which appear as a result of counting single subjects like people, animals, etc. The natural number series is 1, 2, 3, 4, 5, etc.
• Addition


  Finding the sum of some numbers
• Subtraction

  Finding an addend by a sum and another addend
• Multiplication


  Repeating a multiplicand as an addend a certain number of times (the multiplier)
• Division


  Finding one of the factors by a product and another factor
• Raising to a power


  Repeating a number as a factor a certain number of times (the exponent)
• Extraction of a root


  Finding the base of a power by the power and its exponent
• Order of operations

  • Brackets 2) Raising to a power and extraction of a root 3) Multiplication and division 4) Addition and subtraction
• Commutative law of addition


  The sum is not changed by rearranging the addends
• Commutative law of multiplication


  The product is not changed by rearranging the factors
• Associative law of addition


  The sum does not depend on grouping the addends
• Associative law of multiplication


  The product does not depend on grouping the factors
• Distributive law of multiplication over addition


  (m + n) * k = m*k + n*k
• Prime numbers


  Numbers only divisible by 1 and themselves
• Composite numbers


  Numbers with factors other than 1 and themselves
• Factorization


  Expressing a composite number as a product of its prime factors
• Greatest common factor (GCF)


  The largest number that divides each of the given numbers without a remainder
• Finding the GCF

  Express each number as a product of prime factors 2) Write the least power of each common prime factor 3) Multiply these powers
• Least common multiple (LCM)


  The smallest number that is divisible by each of the given numbers
• Finding the LCM

  Express each number as a product of prime factors 2) Write the greatest power of each prime factor 3) Multiply these powers
• Prime factors


  The factors of a number that are prime numbers
• To write out all prime factors


  Presented at least in one of these numbers
• To take the greatest power of each of them


  Meeting in the factorizations
• 504 = 2 · 2 · 2 · 3 · 3 · 7 = 23 · 32 · 71
• 168 = 2 · 2 · 2 · 3 · 7 = 23 · 31 · 71
• 180 = 2 · 2 · 3 · 3 · 5 = 22 · 32 · 51
• 3024 = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7 = 24 · 33 · 71
• Divisibility by 2


  A number is divisible by 2 if its last digit is 0 or is divisible by 2
• Divisibility by 4


  A number is divisible by 4 if its two last digits are zeros or they make a two-digit number divisible by 4
• Divisibility by 8


  A number is divisible by 8 if its three last digits are zeros or they make a three-digit number divisible by 8
• Divisibility by 3 and 9


  A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 9 if the sum of its digits is divisible by 9
• Divisibility by 6


  A number is divisible by 6 if it is divisible by 2 and by 3
• Divisibility by 5


  A number is divisible by 5 if its last digit is 0 or 5
• Divisibility by 25


  A number is divisible by 25 if its two last digits are zeros or they make a number divisible by 25
• Divisibility by 10


  A number is divisible by 10 if its last digit is 0
• Divisibility by 100


  A number is divisible by 100 if its two last digits are zeros
• Divisibility by 1000


  A number is divisible by 1000 if its three last digits are zeros
• Divisibility by 11


  A number is divisible by 11 if the sum of its digits on even places equals the sum of its digits on odd places, or the difference between these sums is divisible by 11
• 378015 is divisible by 3, 5, 11 but not by 2, 4, 6, 8, 9, 10, 25, 100, 1000
• Vulgar (simple) fraction


  A part of a unit or some equal parts of a unit