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Finding Factor PairsFREEWorksheet Generator(Grade 4)

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Level:
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Set A โ€ข 10 Qs
PanMaths.comFinding Factor Pairs Worksheets โ€ข Set A (Medium)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.Find all factor pairs for 48:
Pairs:
Workspace:
2.Find all factor pairs for 63:
Pairs:
Workspace:
3.Find all factor pairs for 40:
Pairs:
Workspace:
4.Find all factor pairs for 64:
Pairs:
Workspace:
5.Find all factor pairs for 70:
Pairs:
Workspace:
6.Find all factor pairs for 24:
Pairs:
Workspace:
7.Find all factor pairs for 54:
Pairs:
Workspace:
8.Find all factor pairs for 72:
Pairs:
Workspace:
9.Find all factor pairs for 42:
Pairs:
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10.Find all factor pairs for 30:
Pairs:
Workspace:
PanMaths.com โ€ข Free Math Worksheet Generator โ€ข Set A (Medium)Page 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Set A (Medium)
Answer Key
Total Problems: 10
1.Find all factor pairs for 48:
Factor Pairs:
1 ร— 48, 2 ร— 24, 3 ร— 16, 4 ร— 12, 6 ร— 8
1. Test whole numbers starting from 1 up to โˆš48 (โ‰ˆ 6):
โ€ข 48 รท 1 = 48 โž” Pair: 1 ร— 48 = 48
โ€ข 48 รท 2 = 24 โž” Pair: 2 ร— 24 = 48
โ€ข 48 รท 3 = 16 โž” Pair: 3 ร— 16 = 48
โ€ข 48 รท 4 = 12 โž” Pair: 4 ร— 12 = 48
โ€ข 48 รท 6 = 8 โž” Pair: 6 ร— 8 = 48
2. Total Factor Pairs for 48: 5 pairs.
3. All Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 โœ…
2.Find all factor pairs for 63:
Factor Pairs:
1 ร— 63, 3 ร— 21, 7 ร— 9
1. Test whole numbers starting from 1 up to โˆš63 (โ‰ˆ 7):
โ€ข 63 รท 1 = 63 โž” Pair: 1 ร— 63 = 63
โ€ข 63 รท 3 = 21 โž” Pair: 3 ร— 21 = 63
โ€ข 63 รท 7 = 9 โž” Pair: 7 ร— 9 = 63
2. Total Factor Pairs for 63: 3 pairs.
3. All Factors: 1, 3, 7, 9, 21, 63 โœ…
3.Find all factor pairs for 40:
Factor Pairs:
1 ร— 40, 2 ร— 20, 4 ร— 10, 5 ร— 8
1. Test whole numbers starting from 1 up to โˆš40 (โ‰ˆ 6):
โ€ข 40 รท 1 = 40 โž” Pair: 1 ร— 40 = 40
โ€ข 40 รท 2 = 20 โž” Pair: 2 ร— 20 = 40
โ€ข 40 รท 4 = 10 โž” Pair: 4 ร— 10 = 40
โ€ข 40 รท 5 = 8 โž” Pair: 5 ร— 8 = 40
2. Total Factor Pairs for 40: 4 pairs.
3. All Factors: 1, 2, 4, 5, 8, 10, 20, 40 โœ…
4.Find all factor pairs for 64:
Factor Pairs:
1 ร— 64, 2 ร— 32, 4 ร— 16, 8 ร— 8
1. Test whole numbers starting from 1 up to โˆš64 (โ‰ˆ 8):
โ€ข 64 รท 1 = 64 โž” Pair: 1 ร— 64 = 64
โ€ข 64 รท 2 = 32 โž” Pair: 2 ร— 32 = 64
โ€ข 64 รท 4 = 16 โž” Pair: 4 ร— 16 = 64
โ€ข 64 รท 8 = 8 โž” Pair: 8 ร— 8 = 64
2. Total Factor Pairs for 64: 4 pairs.
3. All Factors: 1, 2, 4, 8, 16, 32, 64 โœ…
5.Find all factor pairs for 70:
Factor Pairs:
1 ร— 70, 2 ร— 35, 5 ร— 14, 7 ร— 10
1. Test whole numbers starting from 1 up to โˆš70 (โ‰ˆ 8):
โ€ข 70 รท 1 = 70 โž” Pair: 1 ร— 70 = 70
โ€ข 70 รท 2 = 35 โž” Pair: 2 ร— 35 = 70
โ€ข 70 รท 5 = 14 โž” Pair: 5 ร— 14 = 70
โ€ข 70 รท 7 = 10 โž” Pair: 7 ร— 10 = 70
2. Total Factor Pairs for 70: 4 pairs.
3. All Factors: 1, 2, 5, 7, 10, 14, 35, 70 โœ…
6.Find all factor pairs for 24:
Factor Pairs:
1 ร— 24, 2 ร— 12, 3 ร— 8, 4 ร— 6
1. Test whole numbers starting from 1 up to โˆš24 (โ‰ˆ 4):
โ€ข 24 รท 1 = 24 โž” Pair: 1 ร— 24 = 24
โ€ข 24 รท 2 = 12 โž” Pair: 2 ร— 12 = 24
โ€ข 24 รท 3 = 8 โž” Pair: 3 ร— 8 = 24
โ€ข 24 รท 4 = 6 โž” Pair: 4 ร— 6 = 24
2. Total Factor Pairs for 24: 4 pairs.
3. All Factors: 1, 2, 3, 4, 6, 8, 12, 24 โœ…
7.Find all factor pairs for 54:
Factor Pairs:
1 ร— 54, 2 ร— 27, 3 ร— 18, 6 ร— 9
1. Test whole numbers starting from 1 up to โˆš54 (โ‰ˆ 7):
โ€ข 54 รท 1 = 54 โž” Pair: 1 ร— 54 = 54
โ€ข 54 รท 2 = 27 โž” Pair: 2 ร— 27 = 54
โ€ข 54 รท 3 = 18 โž” Pair: 3 ร— 18 = 54
โ€ข 54 รท 6 = 9 โž” Pair: 6 ร— 9 = 54
2. Total Factor Pairs for 54: 4 pairs.
3. All Factors: 1, 2, 3, 6, 9, 18, 27, 54 โœ…
8.Find all factor pairs for 72:
Factor Pairs:
1 ร— 72, 2 ร— 36, 3 ร— 24, 4 ร— 18, 6 ร— 12, 8 ร— 9
1. Test whole numbers starting from 1 up to โˆš72 (โ‰ˆ 8):
โ€ข 72 รท 1 = 72 โž” Pair: 1 ร— 72 = 72
โ€ข 72 รท 2 = 36 โž” Pair: 2 ร— 36 = 72
โ€ข 72 รท 3 = 24 โž” Pair: 3 ร— 24 = 72
โ€ข 72 รท 4 = 18 โž” Pair: 4 ร— 18 = 72
โ€ข 72 รท 6 = 12 โž” Pair: 6 ร— 12 = 72
โ€ข 72 รท 8 = 9 โž” Pair: 8 ร— 9 = 72
2. Total Factor Pairs for 72: 6 pairs.
3. All Factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 โœ…
9.Find all factor pairs for 42:
Factor Pairs:
1 ร— 42, 2 ร— 21, 3 ร— 14, 6 ร— 7
1. Test whole numbers starting from 1 up to โˆš42 (โ‰ˆ 6):
โ€ข 42 รท 1 = 42 โž” Pair: 1 ร— 42 = 42
โ€ข 42 รท 2 = 21 โž” Pair: 2 ร— 21 = 42
โ€ข 42 รท 3 = 14 โž” Pair: 3 ร— 14 = 42
โ€ข 42 รท 6 = 7 โž” Pair: 6 ร— 7 = 42
2. Total Factor Pairs for 42: 4 pairs.
3. All Factors: 1, 2, 3, 6, 7, 14, 21, 42 โœ…
10.Find all factor pairs for 30:
Factor Pairs:
1 ร— 30, 2 ร— 15, 3 ร— 10, 5 ร— 6
1. Test whole numbers starting from 1 up to โˆš30 (โ‰ˆ 5):
โ€ข 30 รท 1 = 30 โž” Pair: 1 ร— 30 = 30
โ€ข 30 รท 2 = 15 โž” Pair: 2 ร— 15 = 30
โ€ข 30 รท 3 = 10 โž” Pair: 3 ร— 10 = 30
โ€ข 30 รท 5 = 6 โž” Pair: 5 ร— 6 = 30
2. Total Factor Pairs for 30: 4 pairs.
3. All Factors: 1, 2, 3, 5, 6, 10, 15, 30 โœ…
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Worksheet Info

Categorygrade-4
Grade LevelGrade 4
DifficultyEasy, Medium, Hard, Sprint
Time5-10 min
CCSS CodeCCSS.MATH.CONTENT.4.OA.B.4

Skills Practiced

  • โœ“ Finding Factor Pairs

Key Strategies

  • ๐ŸŒˆ Factor Rainbow Method: Start with 1 and the number itself on the outside ends of an arc. Move inward one integer at a time (testing 2, 3, 4...) until the factors meet in the middle.
  • ๐Ÿ”ข Systematic Divisibility Testing: Test integers starting from 1 up to the square root of the number (e.g., for 36, stop testing at โˆš36 = 6). If n รท d has no remainder, both d and n รท d form a factor pair.
  • โน๏ธ Square Number Invariant: Square numbers (like 16, 25, 36, 64, 81, 100) have an odd number of total factors because the factor pair contains identical factors (e.g., 6 ร— 6 = 36).
  • ๐Ÿ“ Rectangular Array Models: Visualize factor pairs as the length and width of rectangles that can be formed using n unit squares (e.g., 24 tiles form 1ร—24, 2ร—12, 3ร—8, or 4ร—6 rectangles).
๐ŸŽฎ Interactive Warm-Up

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Related Worksheets

๐Ÿ“œ Standard: CCSS.MATH.CONTENT.4.OA.B.4๐Ÿ”— CCSS.MATH.CONTENT.4.OA.B.4

Mastering Finding Factor Pairs: Core Concepts & Mental Models

Finding factor pairs is a foundational multiplication and division skill under CCSS 4.OA.B.4. Fourth graders learn to systematically pair integers that multiply together to give a target whole number up to 100, understanding that factor pairs reveal the rectangular dimensions of a number and prepare for fractions, prime factorization, and division.

Worked Example & SolutionTeacher Step-by-Step Method
๐Ÿ“ Problem: Find all factor pairs for 36.
Worked Solution: 1. Test 1: 36 รท 1 = 36 โž” Pair: 1 ร— 36. 2. Test 2: 36 รท 2 = 18 โž” Pair: 2 ร— 18. 3. Test 3: 36 รท 3 = 12 โž” Pair: 3 ร— 12. 4. Test 4: 36 รท 4 = 9 โž” Pair: 4 ร— 9. 5. Test 5: 36 รท 5 has a remainder (not a factor). 6. Test 6: 36 รท 6 = 6 โž” Pair: 6 ร— 6. Result: Factor pairs are (1, 36), (2, 18), (3, 12), (4, 9), (6, 6).

๐Ÿ’ก Essential Strategies for Finding Factor Pairs

๐ŸŒˆ Factor Rainbow Method

Start with 1 and the number itself on the outside ends of an arc. Move inward one integer at a time (testing 2, 3, 4...) until the factors meet in the middle.

๐Ÿ”ข Systematic Divisibility Testing

Test integers starting from 1 up to the square root of the number (e.g., for 36, stop testing at โˆš36 = 6). If n รท d has no remainder, both d and n รท d form a factor pair.

โน๏ธ Square Number Invariant

Square numbers (like 16, 25, 36, 64, 81, 100) have an odd number of total factors because the factor pair contains identical factors (e.g., 6 ร— 6 = 36).

๐Ÿ“ Rectangular Array Models

Visualize factor pairs as the length and width of rectangles that can be formed using n unit squares (e.g., 24 tiles form 1ร—24, 2ร—12, 3ร—8, or 4ร—6 rectangles).

โš ๏ธ Common Mistakes & Teacher Fixes

โš ๏ธStopping the search too early and missing intermediate factor pairs (e.g., finding 1ร—24 and 2ร—12 but skipping 3ร—8 and 4ร—6)

Why students stumble: Testing only obvious even divisors (like 2) and forgetting to systematically test 3, 4, etc.

Teacher Fix: Always test consecutive integers starting from 1 up until the numbers meet in the middle (the square root).
Example: For 24: test 1, 2, 3, 4. Stop at 5 because 5 ร— 5 = 25 > 24.
โš ๏ธConfusing factors with multiples (e.g., listing 48, 72 as factor pairs of 24)

Why students stumble: Mixing up numbers that divide INTO 24 (factors) with numbers resulting from multiplying 24 (multiples).

Teacher Fix: Remember: Factors are smaller or equal to the number. Multiples are larger or equal to the number.
Example: Factors of 24 are โ‰ค 24: 1, 2, 3, 4, 6, 8, 12, 24.
โš ๏ธListing duplicate reversed pairs as separate pairs (e.g., listing 3 ร— 8 and 8 ร— 3 as two distinct pairs)

Why students stumble: Applying commutative property without recognizing that (3, 8) and (8, 3) describe the same set of factors.

Teacher Fix: Only list pairs with the smaller number first: write 3 ร— 8 once.
Example: 3 ร— 8 = 24 is one factor pair.

๐Ÿ“– Key Mathematical Vocabulary

Factor

A whole number that divides evenly into another number without leaving a remainder.

Factor Pair

Two whole numbers that multiply together to equal a specific product (such as 3 and 8 for 24).

Factor Rainbow

A visual model connecting paired factors with arcs from the outside ends inward.

Square Number

A number that can be expressed as the product of an integer multiplied by itself (e.g., 36 = 6 ร— 6).

โ“ Frequently Asked Questions

How do you solve a finding factor pairs problem step by step?

Here is a worked example: "Find all factor pairs for 36.". Solution: 1. Test 1: 36 รท 1 = 36 โž” Pair: 1 ร— 36. 2. Test 2: 36 รท 2 = 18 โž” Pair: 2 ร— 18. 3. Test 3: 36 รท 3 = 12 โž” Pair: 3 ร— 12. 4. Test 4: 36 รท 4 = 9 โž” Pair: 4 ร— 9. 5. Test 5: 36 รท 5 has a remainder (not a factor). 6. Test 6: 36 รท 6 = 6 โž” Pair: 6 ร— 6. Result: Factor pairs are (1, 36), (2, 18), (3, 12), (4, 9), (6, 6).

What is the core learning objective for finding factor pairs?

Find all factor pairs for a whole number in the range 1โ€“100, recognize that a whole number is a multiple of each of its factors, and list all factors systematically using factor rainbows or division pairs. This directly aligns with Common Core Standard CCSS.MATH.CONTENT.4.OA.B.4.

What is the most common mistake students make with finding factor pairs?

A frequent pitfall is: "Stopping the search too early and missing intermediate factor pairs (e.g., finding 1ร—24 and 2ร—12 but skipping 3ร—8 and 4ร—6)". Why students stumble: Testing only obvious even divisors (like 2) and forgetting to systematically test 3, 4, etc. How to fix it: Always test consecutive integers starting from 1 up until the numbers meet in the middle (the square root). (Example: For 24: test 1, 2, 3, 4. Stop at 5 because 5 ร— 5 = 25 > 24.)

How does the unlimited finding factor pairs worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of finding factor pairs problems with unique numbers. No two worksheets are ever the same โ€” perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

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Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.