Grade 4 · Operations & Algebraic Thinking · MAT-04-OA-005
Find Factors and Factor Pairs
Represent and solve find factors and factor pairs problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve find factors and factor pairs problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for find factors and factor pairs works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Find Factors and Factor Pairs describes multiplicative structure inside whole numbers. Factor relationships explain exact products and divisibility, while multiples extend repeated equal groups.
Represent the idea
The Math Box uses multiplication grid as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Array Builder
Build equal rows and columns, then connect the grid to repeated addition.
- Build one example of find factors and factor pairs in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
List the factor pairs of 24.
1×24, 2×12, 3×8, 4×6Each pair multiplies exactly to 24; checking only through √24 avoids duplicate reversed pairs.
List the factor pairs of 30.
1×30, 2×15, 3×10, 5×6Each pair multiplies exactly to 30; checking only through √30 avoids duplicate reversed pairs.
List the factor pairs of 36.
1×36, 2×18, 3×12, 4×9, 6×6Each pair multiplies exactly to 36; checking only through √36 avoids duplicate reversed pairs.
List the factor pairs of 40.
1×40, 2×20, 4×10, 5×8Each pair multiplies exactly to 40; checking only through √40 avoids duplicate reversed pairs.
List the factor pairs of 42.
1×42, 2×21, 3×14, 6×7Each pair multiplies exactly to 42; checking only through √42 avoids duplicate reversed pairs.
List the factor pairs of 48.
1×48, 2×24, 3×16, 4×12, 6×8Each pair multiplies exactly to 48; checking only through √48 avoids duplicate reversed pairs.
List the factor pairs of 54.
1×54, 2×27, 3×18, 6×9Each pair multiplies exactly to 54; checking only through √54 avoids duplicate reversed pairs.
List the factor pairs of 56.
1×56, 2×28, 4×14, 7×8Each pair multiplies exactly to 56; checking only through √56 avoids duplicate reversed pairs.
List the factor pairs of 60.
1×60, 2×30, 3×20, 4×15, 5×12, 6×10Each pair multiplies exactly to 60; checking only through √60 avoids duplicate reversed pairs.
List the factor pairs of 63.
1×63, 3×21, 7×9Each pair multiplies exactly to 63; checking only through √63 avoids duplicate reversed pairs.
List the factor pairs of 64.
1×64, 2×32, 4×16, 8×8Each pair multiplies exactly to 64; checking only through √64 avoids duplicate reversed pairs.
List the factor pairs of 72.
1×72, 2×36, 3×24, 4×18, 6×12, 8×9Each pair multiplies exactly to 72; checking only through √72 avoids duplicate reversed pairs.
List the factor pairs of 75.
1×75, 3×25, 5×15Each pair multiplies exactly to 75; checking only through √75 avoids duplicate reversed pairs.
List the factor pairs of 80.
1×80, 2×40, 4×20, 5×16, 8×10Each pair multiplies exactly to 80; checking only through √80 avoids duplicate reversed pairs.
List the factor pairs of 81.
1×81, 3×27, 9×9Each pair multiplies exactly to 81; checking only through √81 avoids duplicate reversed pairs.
List the factor pairs of 84.
1×84, 2×42, 3×28, 4×21, 6×14, 7×12Each pair multiplies exactly to 84; checking only through √84 avoids duplicate reversed pairs.
List the factor pairs of 90.
1×90, 2×45, 3×30, 5×18, 6×15, 9×10Each pair multiplies exactly to 90; checking only through √90 avoids duplicate reversed pairs.
List the factor pairs of 96.
1×96, 2×48, 3×32, 4×24, 6×16, 8×12Each pair multiplies exactly to 96; checking only through √96 avoids duplicate reversed pairs.
List the factor pairs of 100.
1×100, 2×50, 4×25, 5×20, 10×10Each pair multiplies exactly to 100; checking only through √100 avoids duplicate reversed pairs.
List the factor pairs of 108.
1×108, 2×54, 3×36, 4×27, 6×18, 9×12Each pair multiplies exactly to 108; checking only through √108 avoids duplicate reversed pairs.
Practice
Guided practice with hints
01List the factor pairs of 120.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1×120, 2×60, 3×40, 4×30, 5×24, 6×20, 8×15, 10×12
02List the factor pairs of 126.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1×126, 2×63, 3×42, 6×21, 7×18, 9×14
03List the factor pairs of 132.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1×132, 2×66, 3×44, 4×33, 6×22, 11×12
04List the factor pairs of 144.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1×144, 2×72, 3×48, 4×36, 6×24, 8×18, 9×16, 12×12
05List the factor pairs of 150.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1×150, 2×75, 3×50, 5×30, 6×25, 10×15
06List the factor pairs of 160.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1×160, 2×80, 4×40, 5×32, 8×20, 10×16
Practice
Independent practice
01List the factor pairs of 168.
Answer: 1×168, 2×84, 3×56, 4×42, 6×28, 7×24, 8×21, 12×14
02List the factor pairs of 180.
Answer: 1×180, 2×90, 3×60, 4×45, 5×36, 6×30, 9×20, 10×18, 12×15
03List the factor pairs of 192.
Answer: 1×192, 2×96, 3×64, 4×48, 6×32, 8×24, 12×16
04List the factor pairs of 200.
Answer: 1×200, 2×100, 4×50, 5×40, 8×25, 10×20
05List the factor pairs of 24.
Answer: 1×24, 2×12, 3×8, 4×6
06List the factor pairs of 30.
Answer: 1×30, 2×15, 3×10, 5×6
07List the factor pairs of 36.
Answer: 1×36, 2×18, 3×12, 4×9, 6×6
08List the factor pairs of 40.
Answer: 1×40, 2×20, 4×10, 5×8
Common mistakes
Learn to catch the error, not just the answer.
Identify what each number represents and how the quantities are related before selecting an operation.
Estimate, use an inverse operation, or compare with a second representation.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use find factors and factor pairs when solving multi-step problems in measurement, data, money, design, or everyday quantitative decisions.
- Explain the result with units and a second check so another person can audit the reasoning.
Challenge problems
List the factor pairs of 42.
1×42, 2×21, 3×14, 6×7
List the factor pairs of 48.
1×48, 2×24, 3×16, 4×12, 6×8
List the factor pairs of 54.
1×54, 2×27, 3×18, 6×9
List the factor pairs of 56.
1×56, 2×28, 4×14, 7×8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain find factors and factor pairs problems accurately, then check each result with a second method.
Practice
Mastery check
01List the factor pairs of 60.
Answer: 1×60, 2×30, 3×20, 4×15, 5×12, 6×10
02List the factor pairs of 63.
Answer: 1×63, 3×21, 7×9
03List the factor pairs of 64.
Answer: 1×64, 2×32, 4×16, 8×8
04List the factor pairs of 72.
Answer: 1×72, 2×36, 3×24, 4×18, 6×12, 8×9
05List the factor pairs of 75.
Answer: 1×75, 3×25, 5×15
06List the factor pairs of 80.
Answer: 1×80, 2×40, 4×20, 5×16, 8×10
07List the factor pairs of 81.
Answer: 1×81, 3×27, 9×9
08List the factor pairs of 84.
Answer: 1×84, 2×42, 3×28, 4×21, 6×14, 7×12
Terminology
Words to know
- factor
- A whole number that divides another whole number without a remainder.
- multiple
- A product of a number and a whole number.
- prime
- A whole number greater than 1 with exactly two positive factors.
- composite
- A whole number greater than 1 with more than two positive factors.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.