modular arithmetic 3 parts part 1 part 2 part 3 linear congruence

linear congruence example

systems of linear congruences

1. keep dividing prime factor to find largest power divisor trick - very useful!

didn't even realize this apply to the following problem!

How many trailing zeroes are at the end of ( ^{20! /}17! )!?

https://youtu.be/W0RhrFPR5vo?list=PLB6F036DA24898C01

1.

prime factorization - finding factors

total count=product of one more than the exponents

sum=product of the sum of the multiples of each prime,

product=sqrt(number)^count

odd counts=odd prime factors( power+1) product

, even counts= total - odds

sum of proper factors only, not including the number itself

deficient sum<N, not including N itself! 6 is perfect=1+2+3; perfect sum=N; abundant sum>N

prime numbers are always deficient! their factor sum is always 1

[1-2009] how many doesn't have a 1 in it?

1-999 9*9*9=729 -000 =728; 1000-1999 -0;2000-2009 - 9

1. if a positive divisor of 600 is selected at random what is the prob that is prime?
2. how many divisors of 576 are perfect squares?
3. how many divisors does 72^2 have?
4. what is the largest number of primes that could be factors of a number that has 36 factors?
5. how many positive divisors do 1440 and 3024 have in common?

https://youtu.be/6m_5uhnnFuE?list=PLB6F036DA24898C01 on

1. how many even factors does 576 have?
2. find the largest power of 3 that divides 24!

https://youtu.be/W0RhrFPR5vo?list=PLB6F036DA24898C01

keep dividing the prime factor

find largest power of 3 that divides 24!

find largest power of 6 that divides 60!

find the largest power of 72 that divides 80!

find number of factors of 9!

find sum of factors of 9!

find the product of factors of 9!

the remainders when 2 natural numbers are divisible by 12 are 8 and 11 respectively.

find the remainder when their sum is divided by 12.

https://youtu.be/Js3mQSkAQss?list=PLB6F036DA24898C01 on

sequence is list of number, series is adding those numbers

unit digit of exponential

factors that are multiples https://youtu.be/EF46bCwONpo?list=PLB6F036DA24898C01

perfect cube and multiples

perfect square and multiples https://youtu.be/6lI3cfOMVBE?list=PLB6F036DA24898C01

not seen before-

linear congruence https://youtu.be/ptT5j8SwWi8?list=PLB6F036DA24898C01 not seen before

https://youtu.be/uX6xtY_whTc?list=PLB6F036DA24898C01

https://youtu.be/oyISOTnfJEw?list=PLB6F036DA24898C01

90 sprint https://youtu.be/KdqcUByZc1I?list=PLB6F036DA24898C01

base number problem https://youtu.be/4wlpjC-f6MQ?list=PLB6F036DA24898C01

modular arithmetic 3 parts part 3 systems of linear congruences linear congruence

linear congruence example

https://youtu.be/kelBbJ8ZcaE?list=PLB6F036DA24898C01

part 2