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Free printable and online worksheets to help Grade 6 students apply divisibility tests or divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10.

Divisibility tests are handy shortcuts to determine whether a number is divisible by another number (the divisor) without performing actual division. These tests rely on specific patterns observed in the digits of the number.

Here are some common divisibility tests for whole numbers:

Divisibility by 2:

A number is divisible by 2 if the last digit is a 0, 2, 4, 6, or 8. In other words, if the last digit is even.

Divisibility by 3:

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, consider 123: 1 + 2 + 3 = 6, and 6 is divisible by 3, so 123 is also divisible by 3.

Divisibility by 4:

A number is divisible by 4 if the last two digits are divisible by 4.

Divisibility by 5:

A number is divisible by 5 if the last digit is a 0 or a 5.

Divisibility by 6:

A number is divisible by 6 if it’s divisible by both 2 and 3 (refer to the tests for divisibility by 2 and 3).

Divisibility by 8:

A number is divisible by 8 if the last three digits are divisible by 8.
Divisibility by 9:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Benefits of Divisibility Tests:

- Divisibility tests allow for quick mental calculations when performing arithmetic operations. Instead of performing long divisions, you can use divisibility tests to quickly assess whether a number is divisible by another.
- Divisibility tests help in determining the factors of a number or identifying whether a number is prime. By quickly checking divisibility, you can identify potential factors without exhaustive trial and error.
- When simplifying fractions, divisibility tests can help identify common factors between the numerator and denominator, making it easier to simplify fractions to their lowest terms.

Have a look at this video if you need to review how to apply the divisibility tests.

Click on the following worksheet to get a printable pdf document.

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Divisibility Tests Worksheet #1

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Divisibility Rules

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