Printable Number Theory Worksheet | Grade 4 Math

This comprehensive Grade 4 math worksheet provides focused practice on essential number theory concepts. Students will work through six distinct activities covering factors, multiples, prime factorization, and divisibility rules, building a strong foundation for more advanced arithmetic. The ready-to-print PDF format makes it a valuable resource for classroom instruction, review, or homework.

At a Glance

• Grade: 4 · Subject: Math
• Standard: CCSS.MATH.CONTENT.4.OA.B.4 — Gain familiarity with factors and multiples.
• Skill Focus: Factors, Multiples, Prime & Composite Numbers
• Format: 3 pages · 6 problems · Answer key included · PDF
• Best For: Unit review, homework, or math centers
• Time: 25–40 minutes

What's Inside

This three-page PDF includes a two-page worksheet and a full answer key. It is organized into six clear sections: Divisibility Rules, Finding Multiples, Prime Factorization, Identifying Prime and Composite Numbers, Greatest Common Factor (GCF), and Least Common Multiple (LCM). Each part offers several problems for practice.

A Clear Path to Understanding

The worksheet uses a gradual release model. It starts with guided practice in the "Divisibility Rules" section, which acts as a reference. It then moves to supported practice with tasks like "Prime Factorization," which use structured formats like factor trees. Finally, it progresses to independent practice where students must identify prime numbers and solve problems on their own.

Standards Alignment

This worksheet is directly aligned with Common Core State Standard CCSS.MATH.CONTENT.4.OA.B.4, which requires students to find factor pairs, understand multiples, and determine whether a whole number is prime or composite. The tasks provide targeted practice to help students meet the full requirements of this standard. Both standard codes can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

This resource is ideal as a summative review at the end of a number theory unit (25-40 minutes). It also works as a homework assignment. For formative assessment, observe which section is most difficult for students to target re-teaching. Use it after a direct instruction lesson on prime factorization to check for understanding.

Who It's For

Primarily for fourth-graders, this sheet can also challenge third graders or support fifth-grade review. Its clean layout is helpful for all students. For extra support, pair this with a multiplication chart to help students find factors and multiples.

This resource supports the development of number sense, a critical component of mathematical proficiency as outlined by the National Assessment of Educational Progress (NAEP). By focusing on CCSS.MATH.CONTENT.4.OA.B.4, it asks students to gain familiarity with factors and multiples, a gateway skill for fraction and algebra readiness. The worksheet provides the structured, repetitive practice needed for procedural fluency. Research from Fisher & Frey (2014) emphasizes that such independent practice is most effective after students have received direct instruction and engaged in guided practice, a workflow this worksheet naturally supports. The inclusion of six distinct but related tasks helps build cognitive connections between concepts like divisibility, factorization, and primality, reinforcing the underlying structure of the number system and preparing students for more complex mathematical reasoning in later grades.