Factors and multiples is one of the most concept-rich number theory units in Grade 4 math. Fourth graders learn to find all factor pairs of a number, list multiples of a number, classify numbers as prime or composite, apply divisibility rules for 2, 3, 5, 6, 9, and 10, and find the greatest common factor (GCF) and least common multiple (LCM) of two numbers. These skills connect multiplication knowledge to deeper number structure.
The main challenges are confusing factors with multiples, misclassifying 1 and 2 in the prime/composite system, and making errors in factor pair lists by missing factor pairs in the middle. Students also commonly list 24 as 'not divisible by 3' without knowing the digit-sum rule. In Grade 3, students practiced multiplication and division facts; by Grade 5, they will use GCF to simplify fractions and LCM to add unlike fractions.
Our factors and multiples worksheets give fourth graders structured practice correcting factor list errors, identifying prime and composite numbers, applying divisibility rules, matching numbers to their factor counts, finding LCMs, and solving real-world problems that require GCF and LCM reasoning.
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Browse all 12 printable worksheets below — click any card to open the full page.
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
Factors and Multiples
What's Included in This Download
What You'll Learn
These factors and multiples worksheets help grade 4 students develop essential math skills through engaging activities.
Learning Objectives
- Factor Pairs: Find all factor pairs of numbers within 100
- Prime Numbers: Identify prime numbers and explain why they have exactly two factors
- Composite Numbers: Identify composite numbers with more than two factors
- Multiples: List multiples and find common multiples
- Divisibility Rules: Apply rules for 2, 3, 5, and 10
Skills Covered
How to Use These Worksheets
- Download & Print: Click the download button to get the PDF. Print on standard 8.5" x 11" paper.
- Start Simple: Begin with easier pages before moving to more challenging activities.
- Daily Practice: Dedicate 10-15 minutes each day for consistent learning.
- Use Manipulatives: Pair worksheets with physical objects like blocks or counters.
- Provide Encouragement: Celebrate progress and effort to build confidence.
- Check Progress: Use the included answer key to review work together.
Common Mistakes to Watch For
- Missing factor pairs in the middle of a list — students find small factors (1, 2, 3) and large ones (the number itself) but skip middle factors like 4 or 6 in the factors of 24, producing incomplete lists.
- Classifying 1 as prime — students see that 1 has only one factor (itself) and call it prime. But a prime number must have exactly two distinct factors: 1 and itself. The number 1 has only one factor, so it is neither prime nor composite.
- Confusing factors with multiples — students list factors of a number when asked for multiples, or vice versa. A factor divides a number evenly with no remainder; a multiple is the result of multiplying a number by an integer.
Frequently Asked Questions
What is the difference between a factor and a multiple?
A factor of a number divides it evenly with no remainder. For 12, the factors are 1, 2, 3, 4, 6, and 12 — each divides 12 exactly. A multiple of a number is produced by multiplying it by a positive integer. Multiples of 4 are 4, 8, 12, 16, 20 — they go on forever. Think of it this way: factors are smaller than or equal to the number, while multiples are greater than or equal to it.
What is a prime number and what is a composite number?
A prime number has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. The number 2 is the only even prime. A composite number has more than two factors — it can be divided by numbers other than just 1 and itself. Examples: 4, 6, 9, 12. The number 1 is special: it is neither prime nor composite because it has only one factor.
What are divisibility rules?
Divisibility rules let you quickly check whether a number is divisible by another without dividing. A number is divisible by 2 if its last digit is even; by 5 if it ends in 0 or 5; by 10 if it ends in 0; by 3 if its digit sum is divisible by 3 (for 72: 7 + 2 = 9, divisible by 3); by 9 if its digit sum is divisible by 9; by 6 if it is divisible by both 2 and 3.
What is the GCF and how do you find it?
The greatest common factor (GCF) is the largest number that divides two numbers evenly. To find the GCF of 24 and 36: list the factors of each — factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors are 1, 2, 3, 4, 6, 12. The greatest is 12, so GCF(24, 36) = 12. GCF is used to simplify fractions.
What is the LCM and when do you use it?
The least common multiple (LCM) is the smallest number that both numbers divide into evenly. To find the LCM of 4 and 6: list multiples of each — multiples of 4 are 4, 8, 12, 16...; multiples of 6 are 6, 12, 18... The smallest common multiple is 12, so LCM(4, 6) = 12. LCM is used to find a common denominator when adding unlike fractions, and in word problems about events that repeat on different schedules.
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Can I use these in my classroom?
Absolutely! Teachers are welcome to print and use these worksheets in their classrooms. Make as many copies as needed for your students.