Grade 9 & 10 math tutorial on number theory for SAT, Math Kangaroo, and AMC10 Preparation.
In addition to the other topics covered in "Numbers", here are some other commonly used concepts and rules:
- even + even = even
- even + odd = odd
- odd + odd = even
- A-B and A+B have the same parity, ie, they are either odd or even at the same time.
- There is only 1 even prime number, and that is 2.
- For the sume of 2 positive integers A+B to be divisible by another positive integer C, A and B must both be multiples of C.
- Whenever n is the product of three consecutive integers, n is divisible by 6
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Factors
Last modified on 2016-03-02
Factors are the numbers you multiply together to get another number. For example, both 2 and 3 are factors of number 6. And in numberr 8, there are 3 factors that are identical in value: 2, 2, and 2. More...
Prime Factor, Greatest Common Factor, Least Common Multiple
Last modified on 2016-03-02
A Prime number can be divided evenly only by 1 or itself. And it must be a whole number greater than 1.
Prime Factorization is the process of finding all the prime factors of an integer. Here is a simple way. In the first diagram below, the prime factors of integer 891 is 3, 3, 3, 3, and 11. More...
Counting Factors
Last modified on 2016-09-29
How to count the number of factors and prime factors that a positive integer has? Follow this rule:
Let positive integer N = 
, where P1,...,Pk are distinct prime numbers
Number of factors including 1 and N for N is (n1+1) * (n2+1)...(nk+1)
Number of prime factors for N is k
More...
Square & Cube Roots
Last modified on 2016-03-02
A square root of a number is a value that can be multiplied by itself to give the original number. For example, a square root of 9 is 3, because when 3 is multiplied by itself we get 9. Note that -3 is also a square root of 9, because -3 x -3 = 9. More...
Rational & Irrational Numbers
Last modified on 2016-03-02
A Rational number is a real number that can be written as a a simple fraction, a ratio of two integers . An Irrational number is a real number that cannot be written as a simple fraction. More...
Arithmetic Sequence
Last modified on 2013-08-17
A Sequence is a set of things (usually numbers) that are in order.
In an Arithmetic Sequence the difference between one term and the next is a constant.
Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ...
This sequence has a difference of 3 between each number.
Suppose in an arithmetic sequence: More...
Geometric Sequence
Last modified on 2016-03-02
A Sequence is a set of things (usually numbers) that are in order.
In a Geometric Sequence, each term is found by multiplying the previous term by a constant (called “common ratio”).
Example: 2, 4, 8, 16, 32, 64, 128, 256, ... More...
Estimate Square Root
Last modified on 2016-03-02
If you do not have a calculator, you can estimate a decimal approximation of the square root of a number. Here is how, using an example. Suppose you want to know the square root of 20.
You can start out by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5. More...
Conversion between Numerical Notation Systems
Last modified on 2016-07-03
Algorithm to Convert From Another Base to Decimal
To convert hexadecimal, binary, octal, and any other numeric notation systems to decimal nueric notation system More...
