Finding the GCD

Q. What is the greatest common factor of 28 and 42?

Q. There are 32 girls and 40 boys in a class. If they have to stand in equal rows such that each row will only be occupied by either girls or boys, what is the greatest number of students that could be in each row?

1. 22
2. 7
3. 8
4. 6

Q.

Prime factorization of $1000$.

Q. Match the following pairs of numbers with their greatest common divisors.

Number pairs	GCD
(i) 27, 36	(a) 12
(ii) 48, 60	(b) 9

1. (i) and (a), (ii) and (b)
2. (i) and (b), (ii) and (a)
3. (i) and (b), (ii) and (b)
4. (i) and (a), (ii) and (a)

Q.

What is the prime factorization of $125$?

Q. The head of a conference wants to distribute the male and female staff members evenly among all the check-in stations, with no staff members left over. If there are 30 male and 75 female staff members, what is the greatest number of check-in stations that can be set up?

1. 150
2. 5
3. 15
4. 30

Q.

What is the prime factorization of $90$?

Q. Betty wants to plant 72 sunflower saplings and 54 daisy saplings in equal rows such that each row has only one kind of sapling.
What is the greatest number of saplings she can plant in each row?

1. 22
2. 18
3. 9
4. 14

Q. An ice-cube tray is 33 cm long and 11 cm wide. If Gita wants to make ice cubes of equal length and breadth, what is the greatest dimensions of ice cubes she can make such that they fit perfectly into the tray?

1. 10 cm
2. 22 cm
3. 33 cm
4. 11 cm

Q. Lincoln has collected 27 jeans and 45 shirts from his favorite band. He wants to combine them into identical sets to sell, with no pieces left over. What is the greatest number of sets Lincoln can make?

1. 3
2. 9
3. 15

Q. James, Jeremy, and John are placing 105, 112, and 119 traffic cones on different construction sites. If they each want to place equal number of traffic cones on each site, what is the greatest number of traffic cones each site can have?

1. 7
2. 11
3. 21
4. 17

Q. A juice shop makes 8 liters of mango juice, 12 liters of apple juice and 20 liters of orange juice. What is the maximum amount of juice that can be equally filled in containers, such that each container has only kind of juice?

1. 2
2. 3
3. 4
4. 5

Q. 215 crayons, 65 pencils, and 40 paint brushes are to be packed in stationery boxes such that each box has only one kind of item and the number of items in each box is the same.
What is the greatest number of items each box can have?

1. 5
2. 20
3. 15
4. None of the above

Q. Mason has 12 peaches and 18 apples. If he wants to make fruit baskets such that each basket has only one kind of fruit, what is the greatest number of fruits each basket can have?

1. 4
2. 6
3. 8
4. 10