Number Properties Flashcards
AbsVal(n)
The distance n is from 0 on the number line
Prime number definition
A number is prime if it’s only factors are one and itself
What is the only even prime number
2
What is the smallest prime number
2
The 15 prime numbers less than 50
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
10 prime numbers between 50 and 100
53, 59, 61, 67, 71, 73, 79, 83, 89, 97
How to find the total number of factors of a number
Step 1: prime factorize the number
Step 2: add 1 to each exponent from the base numbers in the prime factorization and then multiply the resulting sums together
12: 2^23 -> (2+1)(1+1) -> 6 factors
Prime factorization of n is xy^2z..
How many unique prime factors
3
Prime factorization of n is xy^2z..
How many total prime factors
4
How many prime factors does 1 have?
0, since it can’t be expressed as the product of one or more prime numbers
Lcm
Smallest number into which a set of numbers will divide, or smallest multiple of all numbers in set
Gcf
Largest number that divide evenly into all numbers in a set
How do you find gcf?
Step 1: prime factorize
Step 2: Identify repeated prime factors among the numbers
Step 3: of any repeated prime factors among the #s take only those with the smallest exponent (if no repeated prime factors, gcf is 1)
Step 4: take product of numbers in step 3
Gcf will always be (bigger/smaller) than the largest number in the set?
Smaller
Lcm will always be (bigger/smaller) than the largest number in the set?
Bigger (or equal to)
What does the product of:
LCM(x,y)*GCF(x,y) = ?
x*y
y divides evenly into x translates to…?
x/y
X is divisible by y translates to..?
x/y
x is a dividend of y is synonymous with..?
x is divisible by y
If x is divisible by y, then x is also divisible by some, all, or no factors of y?
All factors of y
If z is divisible by both x, and y, then z is also divisible by..?
LCM of x,y
Z is divisible by 3,4, then z is also divisible by 12
Divisibility rule for 3
If sum of all digits is div by 3
Divisibility rule for 4
If last two digit of number are div by 4
Divisibility rule for 5
If units digit is 0, or 5
Divisibility rule for 6
If number is even and digits sum to a multiple of 3
Divisibility rule for 8
If number is even and last 3 digits are divisible by 8
Is a number ending in 000 divisible by 8?
Yes, all multiples of 1000 are divisible by 8 since 1000 = 125*8
Divisibility rule for 10
If units digit is 0
Divisibility rule for 11
If sum of odd numbered digits - sum of even numbered digits is divisible by 11
Divisibility rule for 12
If number is divisible by both 3, and 4 it is divisible by 12
the product of n consecutive integers is divisibly by..?
n!
Its division results in a decimal remainder, such as 9.48, is it possible to determine the remainder?
No, there are infinite possibilities. You can only go from fraction to decimal remainder, not the other way. Best you can do is convert decimal into reduced fraction, then you would know that the actual remainder is some multiple of that. Ex: 9.48 -> 9(12/25), so remainder is a multiple of 12.
Product of n consecutive even integers is always divisible by ?
(2^n) x n!
For a divisor n, what is the range of possible remainders?
0 through (n-1)
How do you determine the number of trailing zeros in a number
= # of (2,5) pairs in the prime factorization of that number
trailing zeros are created by powers of (what number)
10
520 has one trailing zero and thus has _ power of 10?
5200 has two trailing zeros and thus has _ power of 10?
1 (ie 10 = 10^1)
2 (ie 100 = 10^2)
for any n>=?, n! will have units digit of zero
5, since that product contains a (2,5) pair that yeilds a trailing zero
1/x (where x is a k digit integer that is not a perfect power of 10) has how many leading zeros
k-1
1! = ?
1
0! = ?
1
The prime factorization of a perfect square will contain only (odd/even) exponents?
even
a number squared is a …?
perfect square
prime factorization of a perfecgt cube will only have prime factors with exponenents that are divisible by ?
3
What property of a fraction causes a terminating decimal
if the denominator of the fraction (in its most reduced form) contains only 2’s, 5’s, or both
Do all divisors exhibit remainder patterns?
Yes
When we divide consecutive positive integers by integer n, the remainder pattern will be
0, 1, 2, .. , n-1
when a whole number is divided by 10 what will the remainder be?
the units digit of the dividend. So, 153/10 -> remainder is 3
when a whole number is divided by 10^n, what will the remainder be?
the last n digits of the dividend. So 153/1000 = 153/(10^3) -> remainder is 153
What special pattern arises (re remainders) when integers with the same units digit are divided by 5
the remainder is constant (ex: 9/5 has remainder 4, 19/5 has remainder 4, …)
Two consecutive integers (will/will not) share (some/any) of the same prime factors?
they will not share any of the same prime factors
What is the GCF of two consecutive integers?
GCF(n, n+1) = 1
what is the term for the greatest integer that will divide into a set of numbers?
Greatest common factor
radical(positive number) will (always/sometimes) be positive?
always
what is a whole number?
all positive integers, plus zero (all non-negative integers)
2n represents (even or odd #s) and 2n+1 or 2n-1 represent (even or odd #s)
2n -> even
2n+1 or 2n-1 -> odd
even+/-even = ?
even
odd+/-even = ?
odd
odd+/-odd=?
even
even x [anything] = ?
even
odd x odd = ?
odd
even/even =?
could be odd or even
even/odd = ?
even
odd/odd = ?
odd
why is there no rule for odd/even =?
because an odd number divided by an even number will never be an integer
the word factor is synonymous with what?
divisor
if a set of numbers share no prime factors, what is the LCM of that set of numbers?
the product of the numbers in the set
if there are no repeated prime factors between a set of numbers, what is the GCF of the set?
1
if we know that x/y=int (y divides evenly into x), then the LCM and GCF of the set x and y are?
LCM = x, GCF = y
does the LCM of a set of numbers provide us with all the unique prime factors of the set? if so, what else does it provide us?
yes, and the unique prime factors of the product of the numbers in the set
in a fraction, which of the numerator and denominator is the dividend and which is the divisor?
numerator is the dividend, and denominator is the divisor
what is the units digit of 999^500?
1, since it is a number ending with a units of 9 raised to an even power (just memorize this)
what is the units digit of 999^499
9, since it is a number ending with a units of 9 raised to an odd power (just memorize this)
if we know that positive integer y divides evenly into positive integer x (ie. x/y = int, or x is a multiple of y), then what do we know about the GCF and the LCM of those two numbers?
GCF(x,y) =y, and LCM(x,y)=x
if positive integer N divided by positive integer d leaves remainder r, then the possible values of N are: r, r+d, r+2d, r+3d,….
if positive integer N divided by positive integer j leaves a remainder b, and if N divided by positive integer k leaves a remainder of c, then all possible values of N can be found via the following process:
Step 1: find the smallest possible value of N
Step 2: add the LCM of J and K to this smallest value as many times as necessary
