1. Three pieces of ribbon measuring 75 cm, 105 cm, and 165 cm need to be cut into equal-length pieces without any leftover. What is the longest length of each piece?
2. A gardener has 180 marigold, 240 rose, and 300 sunflower plants. He wants to plant them in rows with the same number of plants in each row and with only one type of plant in each row. What is the maximum number of plants he can plant in each row?
3. Two tankers contain 825 liters and 1155 liters of petrol. Find the maximum capacity of a container that can measure the petrol in whole liters from both tankers exactly.
4. A school is preparing gift packs using 84 pencils, 126 pens, and 210 erasers. Each pack must have the same number of each item, with no leftovers. What is the maximum number of such packs that can be made?
5. A company wants to arrange 120 employees, 180 managers, and 300 workers into equal groups so that each group has the same number of people of each type. What is the largest number of groups possible?
6. A farmer has 360 kg of wheat, 450 kg of rice, and 630 kg of sugar. He wants to pack them into bags of equal weight without mixing. Find the greatest weight that each bag can have.
7.Find the greatest number that divides 289, 334, and 409, leaving the same remainder in each case.
8.A number when divides 1220 and 1420, it leaves remainder 20 in each case. Find the greatest such number.
9.Find the largest number that will divide 200 and 374, leaving remainders 12 and 20 respectively.
10.Find the largest number that divides 289 and 341, leaving remainders 5 and 7 respectively.
11.Find the greatest number that will divide 435 and 697, leaving remainders 9 and 11 respectively.
12.A number divides 1365 and 1567 leaving remainders 5 and 7 respectively. What is the largest possible such number?
13.Find the largest number that divides 1207 and 1855, leaving remainder 11 and 13 respectively.
14.Find the greatest number that divides 1340, 1636, and 2236, leaving remainders 4, 6, and 8 respectively.
15.What is the greatest number that will divide 2345, 3473, and 4981, leaving remainders 5, 7, and 9 respectively?
16.Three numbers when divided by the same number leave remainders 14, 22, and 30 respectively. If the numbers are 798, 986, and 1178, find the greatest such number.