8th Grade Mathematics: Factors and Multiples Review

Vocabulary flashcards covering the fundamental concepts of Factors and Multiples (Çarpanlar ve Katlar), EBOB, EKOK, and Prime Numbers for 8th Grade LGS Mathematics.

Positive Integer Factors (Bölenler)

The numbers that can be multiplied together to equal a specific positive integer; every positive integer can be written as the product of two positive integers.

Rainbow Method (Gökkuşağı Yöntemi)

A technique where factors are listed from smallest to largest, and the product of numbers paired from the outer ends to the center always equals the original number.

Prime Number (Asal Sayı)

Natural numbers greater than $1$ that are only divisible by $1$ and themselves.

The smallest prime number

$2$, which is also the only even prime number.

Initial Prime Numbers

The sequence starts with $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, \text{...}$

Prime Factors (Asal Çarpanlar)

The factors of a number that are prime numbers; these can be found using a Factor Tree (Çarpan Ağacı) or a Division List (Bölen Listesi).

Asal Çarpanlar Algoritması (Prime Factor Algorithm)

A method to find prime factors by writing the number and dividing it by prime numbers in sequence until reaching $1$. For example, for $36$, it is written as $2^2 \times 3^2$.

EBOB (En Büyük Ortak Bölen)

The Greatest Common Divisor; the largest of the common divisors of two or more numbers.

EBOB Problem Clues

Situations involving "whole to parts" (bütünden parçaya), such as distributing grains into bags, planting trees at equal intervals, or cutting rods into equal pieces.

EKOK (En Küçük Ortak Kat)

The Least Common Multiple; the smallest of the common multiples of two or more numbers.

EKOK Problem Clues

Situations involving "parts to whole" (parçadan bütüne), such as counting marbles/walnuts in groups, determining when bells will ring together, or forming a square from small tiles.

Relatively Prime Numbers (Aralarında Asal Sayılar)

Positive integers that have no common divisor other than $1$. The numbers themselves do not need to be prime (e.g., $8$ and $9$).

Consecutive Numbers Property

Consecutive numbers are always relatively prime (e.g., $15$ and $16$).

Consecutive Odd Numbers Property

Consecutive odd numbers are always relatively prime (e.g., $11$ and $13$).

Property of $1$ in Relative Primality

The number $1$ is relatively prime with all positive integers.

EBOB and EKOK for Multiples

If one number is a full multiple of another, their EBOB is the smaller number and their EKOK is the larger number (e.g., EBOB($10, 30$) = $10$, EKOK($10, 30$) = $30$).

EBOB and EKOK for Relatively Prime Numbers

The EBOB of relatively prime numbers is always $1$, and their EKOK is equal to the product of the two numbers.

The Fundamental Relation of EBOB and EKOK

For any two positive integers $A$ and $B$, the formula applies: $A \times B = \text{EBOB}(A, B) \times \text{EKOK}(A, B)$. This means the product of two numbers equals the product of their EBOB and EKOK.