Find the Highest Common Factor (HCF) for each of the following problems using the Division Method (Euclidean Algorithm). Show your working step by step.
Question 1
Find the HCF of 72 and 108.
Question 2
Calculate the HCF of 96 and 144.
Question 3
Find the HCF of 85 and 51.
Question 4
A florist has 126 roses and 90 tulips. She wants to make identical bouquets using all the flowers, with each bouquet having the same number of roses and the same number of tulips. What is the maximum number of bouquets she can make?
Question 5
Find the HCF of 210 and 165.
Question 6
Calculate the HCF of 138 and 222.
Question 7
Find the HCF of 245 and 175.
Question 8
Three ropes of lengths 72 meters, 108 meters, and 180 meters need to be cut into pieces of equal length. What is the maximum possible length of each piece if no rope is wasted?
Question 9
Find the HCF of 119 and 187.
Question 10
Calculate the HCF of 152 and 304.
Question 11
Find the HCF of 385 and 231.
Question 12
A teacher has 204 red pens and 276 blue pens. The pens need to be packed into boxes, with each box containing the same number of red pens and the same number of blue pens. What is the maximum number of boxes that can be packed without any pens left over?
Question 13
Find the HCF of 224 and 168.
Question 14
Calculate the HCF of 323 and 437.
Question 15
Two metal rods measure 392 cm and 476 cm in length. They need to be cut into pieces of equal length, with no metal wasted. What is the maximum possible length of each piece?
