Posts Tagged ‘prime’
Friday, November 13th, 2009
An Overview of Composite Numbers
Description
A detailed tutorial on what composite numbers are. Step by step tutorial including several examples of composite numbers and their definition for reference.
Overview
A composite number is the opposite of a prime number. Some people say they are any number that is not prime, but that is not exactly accurate – negative numbers are not prime (even negative prime numbers), and a composite number is not a negative number, it is a positive number. A composite number is any positive integer that has more divisors than itself and one – which are the only two numbers a prime number can be divided by.
Tags: accurate, arithmetic, composite, examples, integer, negative, number, opposite, positive, prime, real
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Find the Next Term in an Arithmetic Sequence
Description
A detailed tutorial on finding the next term of an arithmetic sequence. Step by step tutorial including several examples of arithmetic sequences for reference.
Overview
Arithmetic sequences are sequences of numbers that are written in a particular pattern. Most problems including an arithmetic sequence don’t include all the terms in the sequence, and you have to find the next one in the sequence. In order to do this, you must find the pattern. The pattern can be anything – the same number could be added, subtracted, mutliplied, or divided from each previous number of the sequence. The previous number could be added to the number after it to come up with the next number. Each number in the sequence could be divisible by the same number. All numbers could be perfect or prime. There are an endless number of patterns, all you have to do is look and then follow that pattern to come up with the next term or terms in the sequence.
Tags: add, arithmetic, divide, mutliply, next, number, pattern, perfect, previous, prime, sequence, subtract, term
Posted in Arithmetic | No Comments »
Tuesday, November 10th, 2009
How to Make Factor Trees
Description
A detailed tutorial on how to make factor trees. Step by step tutorial including several examples on how to make factor trees for reference.
Overview
A factor tree is a type of tree diagram that splits numbers into their factors. It is a very useful method of simplification. First, start with a number and draw two lines from it. Two numbers that when multiplied equal your first number need to go there. A great number to start with is 2, if your number is an even number. you can start with any two numbers you like, provided they fit the guidelines, excluding anything paired with the number one – because then you won’t get anywhere. Then for each of your two numbers, if they are not simplified, you do the same process with them. Keep it up until you are down to simplified, or prime, numbers. You will know you have reached one when the only multiples are one and itself.
Tags: algebra, diagram, even, factor, itself, multiple, number, odd, one, prime, simplification, simplified, simplify, tree, two
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
How to Identify Coprime Numbers
Description
A detailed tutorial on identifying coprime numbers. Step by step tutorial including several examples of how to identify coprime numbers for reference.
Overview
Two numbers are considered to be coprime, or relatively prime, if they have no common positive factor other than 1, or if their greatest common divisor is 1. Sometimes the notation for perpendicular is used to say that a number A is coprime to another number B. The term coprime was invented because the numbers are prime together, but are not prime themselves. A prime number can be coprime with any number.
Tags: arithmetic, common, coprime, divisor, factor, greatest, notation, number, one, perpendicular, positive, prime, relatively
Posted in Arithmetic | No Comments »
Friday, October 9th, 2009
Indentifying Prime Polynomials
Description
A detailed tutorial on how to identify prime polynomials. Step by step tutorial including several examples of identifying prime polynomials for reference.
Overview
Prime polynomials are any polynomial that cannot be factored. Just like a number is prime if you can not break it down into two seperate whole numbers to multiply, a polynomial is prime if you cannot break it down into two separate binomials with whole numbers to multiply. When you run into a prime polynomial when trying to solve a quadratic equation, you cannot use the factoring method. what the factoring method does is split the polynomials into a binomial, which cannot be done to a prime polynomial. If you have a prime polynomial, you have to use the quadratic formula to solve it. At first, you can spot prime polynomials by attempting to factor it, but eventually you will be able to do it just by looking at it.
Tags: algebra, binomial, equation, factoring, formula, Math, multiply, number, polynomial, prime, quadratic, whole
Posted in Algebra | No Comments »
Thursday, October 1st, 2009
Introduction to Fermat’s Last Theorem
Description
A detailed tutorial of Fermat’s Last Theorem. Step by step tutorial including several examples of Fermat’s Last Theorem for reference.
Overview
Fermat’s Last Theorem is one of the most well known mathematical theorems. Fermat’s Last Theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Notice that the pattern for this theorem follows the Pythagorean theorem. This theorem had to be proved for odd prime numbers, as Fermat had only left that there was the special instance of n = 4 that works for this equation. Fermat first came up with the problem in 1637, but it was not solved until 1995. This theorem led to the developement of both algebraic number theory and the proof of the modularity theorem.
Tags: a, algebraic number theory, Andrew Wiles, b, c, Calculus, Fermat's Last Theorem, integers, Math, modularity theorem, n!, numbers, odd, Pierre de Fermat, positive, prime, pythagorean theorem
Posted in Calculus | No Comments »
Thursday, September 24th, 2009
The History of the Number Zero
Description
A detailed tutorial on the history of the number zero. Step by step tutorial including several citations of the history of the number zero for reference.
Overview
Zero is a number we’ve heard about a lot. It’s not a counting number, it’s not negative or positive, it’s not even or odd. It’s not a prime number, it doesn’t even really fit the definitions of a real number or a whole number although it is considered to be both. It is certainly one of the most interesting numbers you can work with. In writing, 0 is distinguished from the capital letter O by either being a bit smaller or having a bit more of an oval shape. Often when handwriting as opposed to typing a line will be drawn through the zero, although this can be confused with an empty set if you are learning set theory. The name zero came from several different lanuages, in which words similar to zero translated to “is empty” “nothing”, and “void”. When doing calculations you must be sure to know the difference between 0 and NaN – “not a number”. Often things that look like they should be zero (0 / 0, for example) are really not numbers at all.
Tags: 0, arithmetic, empty, even, Math, NaN, negative, nil, not a number, nothing, nought, null, number, odd, oh, positive, prime, real, void, whole, zero
Posted in Arithmetic | No Comments »
Tuesday, September 22nd, 2009
Definition of a Prime Number
Description
A detailed tutorial on the solving of prime numbers. Step by step tutorial including several examples of what a prime number is and the definition of a prime number for reference.
Overview
A prime number is a type of number you will hear a lot about. It is any number greater than 1 that is not divisible by anything other than itself and one. This also tells us that it must be a positive number – there are no negative numbers that are greater than 1. Also, except for one prime number, only odd numbers can be prime numbers. This is because all even numbers are divisible by 2. So the only even prime number is 2, which is only divisible by itself and 1. Examples of prime numbers are 2, 3, 5, 7, 11, and 13. You can easily check to see if a larger number is a prime number by using algebra tricks for divisibility. Remember that it must divide evenly – if you get a known fraction or decimal then it is considered to not be divisible by that number.
Tags: decimal, divisibility, even, fraction, greater than 1, Math, non-divisible, number, odd, positive, prime, prime numbers, real, whole
Posted in Arithmetic | No Comments »
