Test 3 Review 2025
GCD or GCF - answer The greatest common divisor (GCD) or the greatest common
factor (GCF) of two whole numbers a and b not both 0 is the greatest whole number that
divides both a and b.
Algorithms for Greatest Common Divisor - answer color Rods, Intersection of sets,
Prime Factorization and Euclidean algorithm
Colored Rods Method - answer Find the GCD of 6 and 8 using the 6 rod and the
8 rod
Color Rod Method Continued - answer Find the longest rod such that we can use
multiples of that rod to build both the 6 rod and the 8 rod. The 2 rods can be used to
build both the 6 and 8 rods.
Color Rod Method Continued 1 - answer The 3 rods can be used to build the 6 rod but
not the 8 rod.
The 4 rods can be used to build the 8 rod but not the 6 rod.
Therefore, GCD(6, 8) = 2.
The Intersection-of-Sets Method - answerList all members of the set of whole number
divisors of the two numbers, then find the set of all common divisors, and, finally, pick
the greatest element in that set
The Intersection-of-Sets Method example - answerTo find the GCD of 20 and 32
The Prime Factorization Method - answerTo find the GCD of two or more non-zero
whole numbers, first find the prime factorizations of the given numbers and then identify
each common prime factor of the given numbers. The GCD is the product of the
common factors, each raised to the lowest power of that prime that occurs in any of the
prime factorizations.
Numbers, such as 4 and 9, whose GCD is 1 are relatively prime
The Prime Factorization Method of find the GCD - answera. GCD(108, 72)
The Prime Factorization Method of find the GCD 1 - answerb. GCD(0, 13)
Because 13 | 0 and 13 | 13, GCD(0, 13) = 13.
Prime Factorization - answer2 numbers who's GCF are 1
Relatively Prime - answertwo whole numbers are relatively prime if they share no
common positive divisors except 1
GCD or GCF - answer The greatest common divisor (GCD) or the greatest common
factor (GCF) of two whole numbers a and b not both 0 is the greatest whole number that
divides both a and b.
Algorithms for Greatest Common Divisor - answer color Rods, Intersection of sets,
Prime Factorization and Euclidean algorithm
Colored Rods Method - answer Find the GCD of 6 and 8 using the 6 rod and the
8 rod
Color Rod Method Continued - answer Find the longest rod such that we can use
multiples of that rod to build both the 6 rod and the 8 rod. The 2 rods can be used to
build both the 6 and 8 rods.
Color Rod Method Continued 1 - answer The 3 rods can be used to build the 6 rod but
not the 8 rod.
The 4 rods can be used to build the 8 rod but not the 6 rod.
Therefore, GCD(6, 8) = 2.
The Intersection-of-Sets Method - answerList all members of the set of whole number
divisors of the two numbers, then find the set of all common divisors, and, finally, pick
the greatest element in that set
The Intersection-of-Sets Method example - answerTo find the GCD of 20 and 32
The Prime Factorization Method - answerTo find the GCD of two or more non-zero
whole numbers, first find the prime factorizations of the given numbers and then identify
each common prime factor of the given numbers. The GCD is the product of the
common factors, each raised to the lowest power of that prime that occurs in any of the
prime factorizations.
Numbers, such as 4 and 9, whose GCD is 1 are relatively prime
The Prime Factorization Method of find the GCD - answera. GCD(108, 72)
The Prime Factorization Method of find the GCD 1 - answerb. GCD(0, 13)
Because 13 | 0 and 13 | 13, GCD(0, 13) = 13.
Prime Factorization - answer2 numbers who's GCF are 1
Relatively Prime - answertwo whole numbers are relatively prime if they share no
common positive divisors except 1
