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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 $2/7$.; The numerator and denominator are positive integers.

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 $2/7$.; The numerator and denominator are positive integers.

To compute $\gcd(5295, 4321)$, apply the Euclidean algorithm by repeatedly dividing the previous divisor by the previous remainder. Start with $5295 = 1 \cdot 4321 + 974$.

Conditions: The inputs are 5295 and 4321.; The Euclidean algorithm is used.; The division algorithm is applied at each step.

To compute $\gcd(5295, 4321)$, apply the Euclidean algorithm by repeatedly dividing the previous divisor by the previous remainder. Start with $5295 = 1 \cdot 4321 + 974$.

Conditions: The inputs are 5295 and 4321.; The Euclidean algorithm is used.; The division algorithm is applied at each step.

The Euclidean algorithm computes the greatest common divisor by repeatedly applying the division algorithm. Starting with two natural numbers $a$ and $b$, you divide the larger by the smaller to get a quotient and a remainder.

Conditions: The inputs $a$ and $b$ are natural numbers.; The division algorithm is applied repeatedly.; The process stops when a remainder equals 0.

The Euclidean algorithm computes the greatest common divisor by repeatedly applying the division algorithm. Starting with two natural numbers $a$ and $b$, you divide the larger by the smaller to get a quotient and a remainder.

Conditions: The inputs $a$ and $b$ are natural numbers.; The division algorithm is applied repeatedly.; The process stops when a remainder equals 0.

Once the new remainder is 0, the division is exact, meaning the current divisor perfectly divides the previous dividend. The algorithm's termination rule states that the greatest common divisor of the original pair is the last nonzero remainder, which is the divisor of this final exact division.

Conditions: The Euclidean algorithm has been applied to two positive integers.; A division step has produced a remainder of 0.; The inputs are 10 and 45.

Once the new remainder is 0, the division is exact, meaning the current divisor perfectly divides the previous dividend. The algorithm's termination rule states that the greatest common divisor of the original pair is the last nonzero remainder, which is the divisor of this final exact division.

Conditions: The Euclidean algorithm has been applied to two positive integers.; A division step has produced a remainder of 0.; The inputs are 10 and 45.

To compute the greatest common divisor of 1785 and 546, apply the Euclidean algorithm by repeatedly dividing the previous divisor by the previous remainder. Start with 1785 divided by 546.

Conditions: The inputs are 1785 and 546.; The Euclidean algorithm is used.; The division algorithm is applied at each step.

To compute the greatest common divisor of 1785 and 546, apply the Euclidean algorithm by repeatedly dividing the previous divisor by the previous remainder. Start with 1785 divided by 546.

Conditions: The inputs are 1785 and 546.; The Euclidean algorithm is used.; The division algorithm is applied at each step.

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.

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.

To begin the Euclidean algorithm for $\gcd(1701, 3768)$, place the larger number (3768) on the left side of the division equation and the smaller number (1701) as the divisor. Write $3768 = 1701 \cdot q + r$.

Conditions: The inputs are positive integers.; The larger number is used first on the left-hand side.; The quotient is an integer and the remainder satisfies $0 \le r < 1701$.

To begin the Euclidean algorithm for $\gcd(1701, 3768)$, place the larger number (3768) on the left side of the division equation and the smaller number (1701) as the divisor. Write $3768 = 1701 \cdot q + r$.

Conditions: The inputs are positive integers.; The larger number is used first on the left-hand side.; The quotient is an integer and the remainder satisfies $0 \le r < 1701$.

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.

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.

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.

To perform each step, you keep the smaller number and subtract it from the larger number. You then replace the larger number with the resulting difference and repeat the process until the desired stopping value is reached.

Conditions: The video explicitly applies this to the pair 12 and 8.; It assumes one chooses the larger and smaller number at each step.

To perform each step, you keep the smaller number and subtract it from the larger number. You then replace the larger number with the resulting difference and repeat the process until the desired stopping value is reached.

Conditions: The video explicitly applies this to the pair 12 and 8.; It assumes one chooses the larger and smaller number at each step.

Trivial factors are the readily available factors 1 and the integer itself. For any positive integer greater than 1, these two factors are distinct.

Conditions: The target is a positive integer greater than 1.

Trivial factors are the readily available factors 1 and the integer itself. For any positive integer greater than 1, these two factors are distinct.

Conditions: The target is a positive integer greater than 1.