Greatest Common Factor

Greatest Common Factor – Definition

The greatest common factor is the greatest whole number which is a factor of each of the two or more numbers.

There is no difference between the Highest Common Factor (HCF) and the Greatest Common Divisor (GCD).

Finding GCF or HCF of Two Numbers

HCF – Solved Examples

1. What is the greatest common factor of 9 and 12?

List the Prime factors of each number.

Prime Factors of 9: 3×3
Prime Factors of 12: 3×2×2

There is one ‘3’ in common.

Therefore, the greatest common factor of 9 and 12 is 3.

2. What is the greatest common factor of 18 and 24?

List the Prime factors of each number.

Prime Factors of 18: 2 ×3× 3
Prime Factors of 24: 2×3×2×2

There is ‘2× 3’ in common.

Therefore, the greatest common factor of 18 and 24 is 6.

Check Point

Question 1

Find the greatest common divisor (GCD) of 70, 215, and 310?

Question 2

What is the greatest common factor (GCF) of 24 and 88?

Question 3

Clinton is making trail mix out of 14 bags of nuts and 16 bags of dried fruit. He wants each new portion of trail mix to be identical, containing the same combination of bags of nuts bags of dried fruit, with no bags left over. What is the greatest number of portions of trial mix Clinton can make?

Question 4

Colton is making emergency preparedness kits to share with friends. She has 25 bottles of water and   35 cans of food, which she would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits Veronica can make?

Question 5

Mrs. Kelly, the geography teacher, collected 36 sedimentary rocks and 92 metamorphic ones. Now she wants to create some identical kits for studying rocks, without having any rocks left over. What is the greatest number of kits she can create?

Grade 6 Science Worksheets

• Inquiry process
• Nature of Science
• Scientific Inquiry
• Inquiry, Analysis and Problem Solving
• Ethical Practices
• Science and Society
• Biotic and Abiotic Factors
• Impact of Organisms
• Adaptation
• Spheres of Earth
• Natural Resources
• Environmental Issues
• Conservation of Earth
• Understanding Technology
• Abilities To Do Technological Design
• Structure of Earth
• Solar System
• Rocks and Fossils
• Earth Systems
• Plate Tectonics
• Evolution
• Magnetic Field of Earth
• Geologic Time
• Materials and Processes That Shape a Planet
• Astronomy
• Ecology
• Energy
• Kinetic and Potential Energy
• Energy Transfer
• Matter and its Structure
• States of Matter
• Physical and Chemical Changes
• Force and Motion
• Electricity and Magnetism
• Wave Interactions
• Sound
• Light
• Introduction to Life Science
• The Origin & History of Life On Earth
• Plant and Animal Cells
• Parts of a Cell
• The Cell Cycle
• How Living Organisms Get Energy
• Classification of Organisms
• How Plants Grow & Reproduce
• The Human Respiratory System
• The Human Cardiovascular System
• The Human Digestive System
• The Human Endocrine Systems
• The Human Nervous System
• The Human Muscular System
• The Human Skeletal System

Grade 6 Math Worksheets

• Probability
• Ratio
• Sequence & Patterns
• Division Word Problems  (New)
• Solving two step equations (New)
• One Step Equation  (New)
• Place Value  (New)
• Two Step Equation  (New)
• To convert percents to decimals and vice versa  (New)
• To convert Percents to Fractions and vice versa  (New)