Divisibility+remainder+ Prime Flashcards
Rule of divisibility of 8
if the integer is divisible by 2 three times, or if the last three digits are divisible by 8.
Divisor
= Factor
If you add or subtract
multiples of N
The result is still the multiple of N
A prime number
Has only 2 factors: 1 and itself
Why 2 is a special number
The only even prime
the factor foundation rule
if a is a factor of b, and b is a factor of c, then a is a factor of c
Dividend = Quotient × Divisor + Remainder
X=aY+r
The greatest common factor (GCF)
the largest divisor of two or more integers; this factor will be smaller than or equal to the starting integers
The least common multiple (LCM)
the the smallest multiple of two or more integers; this multiple will be larger than or equal to the starting integers.
Cách tìm GCF và LCM
Prime Factorization
Length of a number
The number of primes (not necessarily distinct)
Count total number of factor
a^x × b^y × c^z (where a, b, and c are all prime)has has (x + 1)(y + 1)(z + 1) different factors
perfect squares
exp: 4,16. has odd number of factors
N !
is multiple of 1 to N
A/B = a.xxx, 0.xxx?
0.xx=Remainder/Divisor
Rule to add reminder
11%4= 3; 22%4=2; 33%4=3+2%4=1
rule to multiple reminder
11%4=3;22%4=2=> 11*22%4=6%4=2
Negative reminder
(-1)/3=3-1=2
Cycle of power of 2
2,4,8,6
Cycle power of 3
3,9,7,1
Cycle power of 4
4,6
Cycle power of 7
7,9,3,1
Cycle power of 8
8,4,2,6
Trailing zeroes
number of consecutive zeros: n/5 + n/(5^2)+…n/(5^k)
How to calculate Highest power n of x
x/n+ x/(n^2)+…. (với n is prime)
