Free Printable WorksheetMathGrade 5Math Curriculum5.27

5.27 Divisibility Rules for Common Divisors Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 5 Math worksheet provides structured practice on 5.27 Divisibility Rules for Common Divisors. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Skill description: Select the correct answer using divisibility rules (such as 2, 3, 4, 5, 6, 8, 9, and 10) to predict whether a number is divisible without dividing. Choose the statement that best justifies the answer using place-value language and an estimation check. Corresponding standards: Not listed in source.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 5

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 5.27 Divisibility Rules for Common Divisors skill assessments:

Problem 1Difficulty: Mastery

A shopper is packing cans. Each group must be the same size. Without dividing, decide whether 59,551,568 is divisible by 8. Choose the statement that best justifies your answer.

ALook at the last three digits: 573. Since 573 is a multiple of 8, 59,551,568 is divisible by 8. (Hundreds-tens-ones rule.)

BThe ones digit is 8. Since 8 is even, 59,551,568 is divisible by 8. (Ones-place rule.)

CLook at the last two digits: 68. Since 68 is a multiple of 8, 59,551,568 is divisible by 8. (Last-two-digits rule.)

DLook at the hundreds, tens, and ones digits: the last three digits are 568. Since 568 is a multiple of 8, 59,551,568 is divisible by 8. Check: 59,551,000 ends in 000 (a multiple of 8), and adding 568 keeps it a multiple of 8.

Solution & Explanation:Look at the last three digits (hundreds, tens, ones): 568. Since 568 is a multiple of 8, 59,551,568 is divisible by 8.

Problem 2Difficulty: Mastery

A class is counting stickers. Each group must be the same size. Without dividing, decide whether 48,873,822 is divisible by 2. Choose the statement that best justifies your answer.

AThe tens digit is 2. Since 2 is odd, 48,873,822 is divisible by 2. (Estimate: tens place controls divisibility.)

BAdd the digits to get 46. Because 46 is a multiple of 2, 48,873,822 is divisible by 2. (Digit-sum rule.)

CThe ones digit is 2, which is even, so 48,873,822 is divisible by 2. Check by place value: 48,873,822 = 48,873,820 + 2, and both parts are even.

DThe ones digit is 2. Since 2 is even, 48,873,822 is not divisible by 2. (Estimate: an odd number is close to 48,873,821.)

Solution & Explanation:Check the ones digit. 48,873,822 ends in 2, which is even. So it is divisible by 2.

Problem 3Difficulty: Mastery

A coach is grouping jerseys. Each group must be the same size. Without dividing, decide whether 44,496,355 is divisible by 9. Choose the statement that best justifies your answer.

AThe ones digit is 5. Since 5 is 9, 44,496,355 is divisible by 9. (Ends-in-9 rule.)

BAdd the digits: 40 is not a multiple of 9, so 44,496,355 is not divisible by 9. Check: 44,496,355 = 44,496,000 + 355; 44,496,000 is divisible by 9 (its thousands part is a multiple of 9), but 355 is not.

CAdd the digits to get 43. Since 43 is a multiple of 9, 44,496,355 is divisible by 9. (Digit-sum rule.)

DLook at the last three digits: 364. Since 364 is a multiple of 9, 44,496,355 is divisible by 9. (Last-three-digits rule.)

Solution & Explanation:Add the digits of 44,496,355. The sum is 40. Because 40 is not a multiple of 9, the number is not divisible by 9.

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