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Yes, in this context, "greatest common factor" is being used for what is more commonly called the greatest common divisor in many modern texts. The mathematical procedure shown is the same subtraction-based Euclidean algorithm.
Conditions: Used informally in the explanation of why the algorithm works.
The speaker verbally says "greatest common denominator," but the mathematical notation on the board is "gcd," which conventionally stands for "greatest common divisor." The context of dividing integers to find a common factor confirms that the intended concept is the greatest common divisor, and the spoken word is a verbal slip.
Conditions: The video discusses finding the common factor of two integers.; The board displays the notation gcd(a;b).; The procedure involves repeated integer division.
It means that the numerator 2 and the denominator 7 have no common positive divisor greater than 1. Their greatest common factor is 1, so the fraction cannot be reduced any further.
Conditions: The fraction is .; The numerator and denominator are positive integers.
The greatest common factor (GCF) is the largest positive divisor shared by all of the compared positive integers. It is the maximum value in the set of their common factors.
Conditions: At least two positive integers are compared.; Positive divisors are compared.
When the Euclidean algorithm yields a greatest common divisor of 1, it means the two input numbers are relatively prime (or coprime). This indicates that they share no common positive integer divisors other than 1.
Conditions: The inputs are natural numbers.; The Euclidean algorithm terminates with a last nonzero remainder of 1.
In this video, the Euclidean algorithm is introduced as a method for finding the greatest common factor of two numbers. The presentation specifically demonstrates the subtraction version of the algorithm rather than the modulo version.
Conditions: Applies to two numbers in the worked example.; The video uses positive integer examples.