1.What is the greatest common divisor of 36 and 84?
2.Find the highest common factor (H.C.F) of the following numbers: 4 × 27 × 3125, 8 × 9 × 25 × 7, and 16 × 81 × 5 × 11 × 49.
3.What is the simplest form of the fraction 1095/1168?
4.Which number among the following has the greatest quantity of divisors?
5.Which of the following represents the prime factorization of 252?
6.A beverage seller has 80 liters of Maaza, 144 liters of Pepsi, and 368 liters of Sprite. He plans to package them into cans so that each can holds the same volume of a single drink without mixing different beverages. What is the minimum total number of cans needed?
7.A rectangular room measures 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. What is the minimum number of square tiles, all of the same size, needed to completely cover the floor?
8.What is the largest number that, when dividing 47, 215, and 365, leaves the same remainder in each instance?
9.What is the largest number that, when dividing 19, 83, and 67, leaves a remainder of 3 each time?
10.What is the largest number that divides 35, 91, and 840 without leaving a remainder?
11.What is the smallest four-digit number that leaves a remainder of 2 when divided by 3, 4, or 5?
12.What is the largest four-digit number that is divisible by 3, 4, and 5 without any remainder?
13.What is the smallest number that, when you add 5 to it, becomes divisible by 6, 9, 15, 20, and 24?
14.A gardener was tasked with planting flowers in rows, each row containing the same number of plants. When he arranged them in rows of 6, 8, 10, or 12, there were always 5 plants left unplanted. However, when he planted them in rows of 13, no plants remained unplanted. How many plants did the gardener have in total?
15.What is the radius of a sphere if its volume and surface area have the same numerical value?
16.A right circular cylinder and a right circular cone share the same radius and volume. What is the ratio of the cylinder's height to the cone's height?
17.A sphere and a right circular cylinder have identical radii, and their volumes are equal. What is the height of the cylinder in terms of its radius?
18.How many solid spheres with a diameter of 6 cm can be formed by melting a solid metal cylinder measuring 45 cm in height and 4 cm in diameter?
19.What is the length of a wire with a radius of 0.2 mm that can be formed by melting a solid copper sphere with a diameter of 18 cm?
20.If the radius of a wire is reduced to one-third of its original size while keeping the volume constant, by what factor will its length change?