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# Number Theory - SHS

### Number Theory and Divisibility - SHS Freshmen Math Team

Divisibility Rule: 2 The last digit is even
Divisibility Rule: 3 The sum of the digits is divisible by three
Divisibility Rule: 4 The last two digits are divisble by 4 (#: abc, bc is divisible by 4)
Divisibility Rule: 5 The last digit is 5 or 0
Divisibility Rule: 6 The number is divisible by both 2 and 3
Divisibility Rule: 7 Double the last digit and subract from the rest of the number, if the result is divisible by7, then the number is divisble by 7 (#: abc, ab-2c is divisible by 7)
Divisibility Rule: 8 The number is divisible by both 2 and 4
Divisibility Rule: 9 The sum of the digits is divisible by 3
Number Cycles: Powers of 2 4 cycles: 2,4,8,6
Number Cycles: Powers of 3 4 cycles: 3,9,7,1
Number Cycles: Powers of 4 2 cycles: 4,6
Number Cycles: Powers of 5 Always ends in 5
Number Cycles: Powers of 6 Always ends in 6
Number Cycles: Powers of 7 4 cycles: 7,9,3,1
Number Cycles: Powers of 8 4 cycles: 8,4,2,6
Number Cycles: Powers of 9 2 cycles: 9,1
Prime Number A Number whose only factors are 1 and itself
Composite Number A Number who has more factor pairs than just 1 and itself
Abundant Number A Number whose value is less than the sum of its factors (excluding itself)
LCM Least Common Multiple, The lowest number that is divisible by both numbers in the given pair
GCD Greatest Common Divisor, the greatest number that both numbers in a given pair are divisible by
Trailing Zeroes Chains of zeroes that occupy the farthest right digits in a (Usually long) number
The Number of Trailing Zeroes (x=#) 10^x
Prime Numbers Less Than 100 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,51,53,59,61,67,71,73,79,83,87,89,97
6 Factorial (Expanded Form) 6*5*4*3*2*1 = 720
Created by: Vingkan