Word Problems on GCD

Q.

There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit?

1. $6720$

2. $60480$

3. $30$

4. $346$

Q.

Find the H.C.F of $64,32$ using prime factorisation and listing factors method.

Q. There are 435 representatives and 100 senators serving in the United State congress. If we want to make the largest number of committees possible with equal number of representatives in each committee and an equal number of senators in each committee, how many committees can we make?

1. 5

Q. You have to pack some fruit baskets from a bunch of 6 apples and 4 oranges, such that apples and oranges are distributed equally. Each basket should contain equal number of apples and equal number of oranges. What should be the minimum number of apples and oranges in each basket?

1. Apples: 3, Oranges: 2
2. Apples: 2, Oranges: 3
3. Apples: 4, Oranges: 1
4. Apples: 1, Oranges: 4

Q. A gift shopkeeper has 45 identical balls, 50 identical toys, 30 identical flowers and 35 identical sweeets. He decides to make maximum number of identical giftboxes having all given items. The total number of items in each giftbox would be .

Q.

Let $n$ be the smallest composite number such that it can be written as the product of two positive integers that differ by $10.$ How many distinct prime factors does $n$ have?

Q. You need to cover a floor of dimension $8\times 4$ $m^2$ with largest possible square tiles. Find the dimension of each tile.

1. $1\times 1$ $m^2$
2. $2\times 2$ $m^2$
3. $3\times 3$ $m^2$
4. $4\times 4$ $m^2$

Q. You are provided a plot of land of dimension $12\times 9{\text{m}}^2$ to plant flower saplings. Each sapling needs to be planted in seperate flower vase of square shape. Find the minimum number of identical flower vases required to cover the whole plot.

1. 3
2. 9
3. 12
4. 24

Q. A penguin ski club is preparing identical lunch boxes for new skiers. They have 60 corn on the cobs and 48 fish sticks. They make lunch boxes by distributing all the corn & fish sticks amongst themselves; there is an equal number of corn on the cobs in each box and an equal number of fish sticks in each box. If they want the largest number of boxes possible, how many corn on the cobs and fish sticks would be in each lunch box repectively?

1. 12
2. 5 and 4
3. 4 and 5
4. 60 and 48

Q. Equal sizes of ribbon tape are to be cut from two cotton rolls of length $16\text{m}$ and $18\text{m}.$ Find the largest size of the ribbon tape such that there is no leftover.

1. 1 m
2. 2 m
3. 3 m
4. 4 m

Q. A farmer decides to build an orchard with 32 orange trees, 24 mango trees and 40 pear trees. If each row has a similar type of fruit tree and equal number of fruit trees, the minimum number of possible rows is .

Q. A penguin ski club is preparing identical lunch boxes for new skiers. They have 60 corn on the cobs and 48 fish sticks. They make lunch boxes by distributing all the corn & fish sticks amongst themselves; there is an equal number of corn on the cobs in each box and an equal number of fish sticks in each box. If they want the largest number of boxes possible, how many corn on the cobs and fish sticks would be in each lunch box repectively?

1. 12
2. 5 and 4
3. 4 and 5
4. 60 and 48

Q. Find the smallest two numbers, neither of which is 8, but their GCD is 8.

1. 16 and 24
2. 24 and 40
3. 8 and 24

Q. $600$ males and $492$ females need to be transported from an island via sea. Find the maximum number of trips required if number of males and number of females in each trip remains constant.

1. $6$
2. $4$
3. $10$
4. $12$

Q. 600 males and 492 females need to be transported from an island via sea. In each trip, number of males transported are same, and also number of females transported are same. The minimum number of passengers per trip is .