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• Pre algebra
• Whole numbers
• Greatest common divisor (GCD)

# Greatest common divisor (GCD)

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•  Question 1: 1 pts Compute:
$GCD(9,6)=$
•  Question 2: 1 pts $a$ and $b$ are relatively prime if $GCD(a, b) = 1.$
•  Question 3: 1 pts Is the following expression true? $$GCD(8,9)=1$$
•  Question 4: 1 pts Let $a$ and $b$ be whole numbers, not both 0. Then, $$GCD(a,b)\geq 0.$$
•  Question 5: 2 pts How is called the procedure shown in the picture?
 Euclidean algorithm The Sieve of Eratosthenes Bezout's identity Teorema de Pitagoras
•  Question 6: 2 pts Use the Euclidean Algorithm, shown on the picture, to compute the greatest common divisor of the numbers $1356$ and$414.$
$GCD(1356,414)=$
•  Question 7: 2 pts Compute the greatest common divisor of $a$ and $b$ if $a=2^{2}\cdot 3\cdot 5^{2}$ and $b=3^{2}\cdot 5.$
 $3^{2}\cdot 5$ $3\cdot 5$ $3\cdot 5^{2}$ $3^{0}\cdot 5$
•  Question 8: 2 pts Compute:
$GCD(12,16,20,28)=$
•  Question 9: 3 pts Determine all the values $x$ for which it is $GCD(9,x)=9, 0 \leq x\leq 45.$
 $1,9,18,27,36$ $0,9,18,27,36$ $0,9,18,27,36,45$ $9,18,27,36,45$
•  Question 10: 3 pts There are 32 forwards and 80 guards in Leo's basketball league. Leo must include all players on a team and wants each team to have the same number of forwards and the same number of guards. What is the greatest number of teams possible?
 $32$ $24$ $16$ $8$
•  Question 11: 3 pts Rafaela is going to plant $63$ tomato plants and $90$ potato plants. She would like to plant the plants in rows where each row has the same number of tomato plants and each row has the same number of potato plants. What is the greatest number of rows she can plant?
 $9$ $8$ $7$ $6$
•  Question 12: 3 pts Seller Lucy in the flower shop currently has $12$ lilies, $16$ roses, and $32$ chrysanthemums. What is the greatest number of equal bouquets that Lucy can make of that flower and how much chrysanthemum will be in each of the same bouquets?
 Number of bouquets $7$, number of chrysanthemums in each bouquet $5$. Number of bouquets $5$, number of chrysanthemums in each bouquet $7$. Number of bouquets $4$, number of chrysanthemums in each bouquet $8$. Number of bouquets $8$, number of chrysanthemums in each bouquet $4$.