# Posts Tagged: "number theory"

## Least Common Multiple

- - Pre-Algebra

The least common multiple (LCM) of two or more numbers is the smallest or least number that is divisible by all the given numbers. Hence, for counting numbers p and q, $p\times q=GCF\left (p,q\right )\times LCM\left (p,q\right ).$

## Greatest Common Factor

- - Pre-Algebra

The greatest common factor (GCF) of two or more counting numbers is the greatest counting number that divides all the given numbers. If that number is 1, then the two numbers are said to be relatively prime.

## Factoring Monomials

- - Pre-Algebra

Factoring monomials is the same thing with factoring numbers. In our previous discussion of factoring, any integer can be written uniquely as a product of prime factors. Hence, the "prime factorization" of a monomial is writing its expression as a product of prime numbers, single variables, and (possibly) a –1.

## Factoring Integers

- - Pre-Algebra

You will recall that, when two or more numbers are multiplied to form a product, they are called the factors of the product. When we start with a product and break it up into factors, the process is called factoring.

In any reference to factors, two factors are considered essentially the same if one is merely the negative of the other.

An integer is said to be prime if it has no integer as a factor except itself or 1. For examples; 2, 3, 5, 7, 11, 13, 17, 19, etc., are prime numbers. In other words, prime numbers must be a whole number greater than 1.

## Factors and Divisibility Rules

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As we all know, a factor is one of two or more quantities that divides a given quantity without a remainder. For example, 3 and 7 are factors of 21; x and y are factors of xy. Concept of factors is a pre-requisite in studying divisibility rules. It is also important in determining whether a certain number is prime or composite.