Free GCD/HCF Worksheets (Grades 4-6)

Practice gcd/hcf (Grades 4-6) with free printable PDF worksheets. 4 pre-packaged classroom sets with 100% verified step-by-step answer keys, plus an unlimited live customizer for teachers and homeschoolers.

⚡ Custom StudioWant custom problem counts (6–50) or fresh numbers?

Launch Free Customizer →

Include Key in PrintShow Worked Steps

⚡ Unlimited & Shuffle →

PanMaths.comGCD/HCF Worksheets • Set A (Standard)

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 10

Directions: Solve each problem carefully. Show all intermediate work in the workspace provided.

1.Find the GCD of 19 and 8

Answer:

________________

2.Find the GCD of 21 and 29

Answer:

________________

3.Find the GCD of 18 and 16

Answer:

________________

4.Find the GCD of 20 and 6

Answer:

________________

5.Find the GCD of 27 and 28

Answer:

________________

6.Find the GCD of 9 and 23

Answer:

________________

7.Find the GCD of 18 and 19

Answer:

________________

8.Find the GCD of 29 and 13

Answer:

________________

9.Find the GCD of 16 and 11

Answer:

________________

10.Find the GCD of 29 and 22

Answer:

________________

PanMaths.com • Free Printable Math WorksheetsPage 1 of 2

PanMaths.comAnswer Key & Worked Solutions • Set A (Standard)

Answer Key

Total Problems: 10

Teacher & Parent Guide: Intermediate evaluation steps are provided for step-by-step grading and student self-correction.

1.Find the GCD of 19 and 8

Answer:

1. Factors of 19: 1, 19

2. Factors of 8: 1, 2, 4, 8

3. Only Common Factor is 1 ➔ GCD(19, 8) = 1 (Co-prime) ✅

2.Find the GCD of 21 and 29

Answer:

1. Factors of 21: 1, 3, 7, 21

2. Factors of 29: 1, 29

3. Only Common Factor is 1 ➔ GCD(21, 29) = 1 (Co-prime) ✅

3.Find the GCD of 18 and 16

Answer:

1. Factors of 18: 1, 2, 3, 6, 9, 18

2. Factors of 16: 1, 2, 4, 8, 16

3. Common Factors: 1, 2 ➔ Greatest is 2 ✅

4.Find the GCD of 20 and 6

Answer:

1. Factors of 20: 1, 2, 4, 5, 10, 20

2. Factors of 6: 1, 2, 3, 6

3. Common Factors: 1, 2 ➔ Greatest is 2 ✅

5.Find the GCD of 27 and 28

Answer:

1. Factors of 27: 1, 3, 9, 27

2. Factors of 28: 1, 2, 4, 7, 14, 28

3. Only Common Factor is 1 ➔ GCD(27, 28) = 1 (Co-prime) ✅

6.Find the GCD of 9 and 23

Answer:

1. Factors of 9: 1, 3, 9

2. Factors of 23: 1, 23

3. Only Common Factor is 1 ➔ GCD(9, 23) = 1 (Co-prime) ✅

7.Find the GCD of 18 and 19

Answer:

1. Factors of 18: 1, 2, 3, 6, 9, 18

2. Factors of 19: 1, 19

3. Only Common Factor is 1 ➔ GCD(18, 19) = 1 (Co-prime) ✅

8.Find the GCD of 29 and 13

Answer:

1. Factors of 29: 1, 29

2. Factors of 13: 1, 13

3. Only Common Factor is 1 ➔ GCD(29, 13) = 1 (Co-prime) ✅

9.Find the GCD of 16 and 11

Answer:

1. Factors of 16: 1, 2, 4, 8, 16

2. Factors of 11: 1, 11

3. Only Common Factor is 1 ➔ GCD(16, 11) = 1 (Co-prime) ✅

10.Find the GCD of 29 and 22

Answer:

1. Factors of 29: 1, 29

2. Factors of 22: 1, 2, 11, 22

3. Only Common Factor is 1 ➔ GCD(29, 22) = 1 (Co-prime) ✅

PanMaths.com • Answer Key & SolutionsPage 2 of 2

✨

Need a Multi-Topic Math Test?Combine GCD/HCF Worksheets with other math skills into a custom 15-to-25 question test with 1-click dual-set anti-cheat PDFs & tablet quizzes.

Build Custom Quiz ➔

PDF + Answer Keys

⭐ Master PDF Workbook$3.99

Multiplication Times Tables 50-Worksheet Master Workbook

✓50 curated printable worksheets in 1 PDF
✓100% verified step-by-step answer keys
✓Unlimited classroom & homeschool print license

🛒 Download 50-Worksheet Pack ($3.99) →

🔒 Instant PDF Download • Secure Checkout via Gumroad & PayPal

💡

How to Create & Print Custom Worksheets in 3 Steps

Every generated sheet includes student name, date, score lines, and a complete answer key!

1⚙️

1. Set Options & Count

Select difficulty (Easy, Medium, Hard) and choose your exact problem count (8, 12, 16, or 20 problems per sheet).

2🎲

2. Generate & Review

Click "Shuffle" to generate fresh randomized questions. Student name, date, and score blanks are added automatically.

3🖨️

3. Print with Answer Key

Print clean 8.5"×11" pages. Includes a detachable verified answer key for 1-minute grading or student self-checking!

⭐

What Every Sheet Includes: Name & Date headers, organized problem numbering, ample student write-in workspace, and a step-by-step verified grading key!

🏫

Recommended Classroom & Homeschool Uses

Versatile math practice formats designed for busy educators and parents.

☀️

Bell Work & Warm-Ups

Quick 5-minute timed drills to start math class with focus.

🎯

Learning Centers

Laminate with dry-erase markers for reusable station practice.

🏠

Homework & Review

Send home with detachable answer keys for easy parent review.

📊

Quizzes & Exit Tickets

Assess student concept retention before chapter tests.

🔗

Explore Interactive Tools for GCD/HCF Worksheets

Master this math concept across all PanMaths learning verticals:

🧮

Calculator Mode

Interactive Step-by-Step Solver

Open →

Worksheet Info

Categoryarithmetic

Grade LevelGrades 4-6

DifficultyCustomizable

Time10-15 minutes

Skills Practiced

✓ Math fluency
✓ Mental math speed

Related Worksheets

📄 Cube Root (∛x)View →📄 Factorial (n!)View →📄 Adding and Subtracting IntegersView →📄 Multiplying and Dividing IntegersView →

💡 1. What is the GCD (HCF)?

The Greatest Common Divisor (also called Highest Common Factor / HCF) is the largest integer that divides both numbers evenly without a remainder.

💡 2. Method 1: Prime Factorization

Find the prime factors of both numbers. Multiply the common prime factors: 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. Common: 2 × 3 = 6.

💡 3. Method 2: The Euclidean Algorithm (Fastest for Big Numbers)

Divide the larger number by the smaller: 75 mod 45 = 30, then 45 mod 30 = 15, then 30 mod 15 = 0. The last non-zero remainder is 15!

Worksheet Facts by Grade Level

Grade Level	Divisor & Factor Goal	Target Pairs
Grade 4	Find all factor pairs for a whole number in the range 1-100	Pairs within 24 (e.g. 12, 18)
Grade 5	Use common factors to simplify fraction answers	Pairs within 60 (e.g. 36, 48)
Grade 6	Find the greatest common factor of whole numbers $le 100$ (CCSS.6.NS.B.4)	Pairs up to 150 (e.g. 72, 120)

Why Mastering the GCD is Essential for Fraction Mastery

The Greatest Common Divisor (GCD) is the foundational engine of fraction simplification. To reduce any fraction a/b to its lowest terms in a single step, divide both the numerator and denominator by GCD(a, b).

Our free printable GCD worksheets provide dual solution proofs on every answer sheet: the Prime Factorization Tree and the Euclidean Remainder Algorithm, giving students deep conceptual and algorithmic insight.

Worked Example: Find GCD(24, 36)

List Prime Factors:
- 24 = 2 × 2 × 2 × 3 = 2³ × 3¹
- 36 = 2 × 2 × 3 × 3 = 2² × 3²
Take Lowest Power of Shared Primes: 2² × 3¹ = 4 × 3 = 12.
Result: GCD(24, 36) = 12.

GCD vs. LCM: Know the Difference

GCD (Greatest Common Divisor): The largest shared factor (≤ smaller number). Used for simplifying fractions.
LCM (Least Common Multiple): The smallest shared multiple (≥ larger number). Used for finding common denominators.
Golden Formula: GCD(a, b) × LCM(a, b) = a × b.

Benefits of Mastery

🍕 Instant Fraction Simplification

Enables 1-step reduction of any rational fraction to irreducible lowest terms.

🌳 Prime Factorization Mastery

Builds automaticity with factor trees, exponents, and prime numbers.

🏛️ Classical Euclidean Algorithm

Introduces one of the oldest and most elegant algorithms in human mathematics.

📋 Standardized Test Alignment

Directly targets Grade 6 Common Core and middle-school competition math.

Frequently Asked Questions

What is the difference between GCD and HCF?

They are identical! "GCD" (Greatest Common Divisor) is the standard term in the US and Canada, while "HCF" (Highest Common Factor) is standard in the UK, India, Australia, and Singapore.

What Common Core standard covers GCD / HCF?

Aligned with CCSS.MATH.CONTENT.6.NS.B.4: "Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12."

What happens if two numbers share no prime factors?

Their GCD is 1. Numbers with GCD = 1 are called "co-prime" or "relatively prime" (e.g. 8 and 15).