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R13 - Number Properties (3/6)
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Factorials, ODD/EVEN
Terms in this set (12)
"By which factors of the following factorials divisible:
1) 10! + 7 = n
2) 10! + 15 = n
3) 10! + 11! = n"
"n is divisible by all factors of 10! And:
1) 7
2) 3, 5 and 15 (because 10! Has both factors of 15)
3) every integer between 1 and 10"
N! is _____ of all integers from 1 to N.
A MULTIPLE
ODD/EVEN: General formula
"The ""divisibility by 2"" determines, if a factor is ODD or EVEN.
EVEN: n=2k
ODD: n=2k+1
Note: 0 = even, and k = integer"
"ODD/EVEN: Arithmetic Operations (1/3)
Addition/subtraction"
" - Same type - always even
- Different type - always odd
a) EVEN +/- EVEN = EVEN
b) ODD +/- ODD = EVEN
c) EVEN +/- ODD = ODD"
"ODD/EVEN: Arithmetic Operations (2/3)
Multiplication"
"1) Rules for multiplication:
a) Any integers is even = EVEN
b) All integers are odd = ODD
EVEN * EVEN = EVEN
EVEN * ODD = EVEN
ODD * ODD = ODD
2) The number of even integers included, gives you additional information about the result:
a) If TWO integers even = result divisible by 4
b) If THREE integers even = result divisible by 8"
"ODD/EVEN: Arithmetic Operations (3/3)
DIVISION:
1) ODD/EVEN
2) EVEN/ODD
3) ODD/ODD"
"Division of two integers can result into an even integer, odd integer or a fraction. There are several potential outcomes, depending upon the value of the dividend and divisor:
1) no integer
2) EVEN/no integer
3) ODD/no integer"
The sum of any two primes will be ____, unless ______.
The sum of any two primes will be even, unless one of the two primes is 2.
If 2 cannot be one of the primes in the sum, the sum must be _____.
If 2 cannot be one of the primes in the sum, the sum must be even.
Characteristic of a perfect square
" - A perfect square has an odd number of prime factors, because in one factor pair x=y
- There are two copies of each prime factor within a perfect square (3 in a cube)"
Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
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