Divisibility Algebra Quiz: Master Divisibility Algebra Quiz

  • 7th Grade
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| Questions: 20 | Updated: Dec 17, 2025
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1) A number n is divisible by 4. Which equation represents this?

Explanation

Divisible by 4 means n is a multiple of 4, so n = 4k for some integer k.

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About This Quiz
Divisibility Algebra Quiz: Master Divisibility Algebra Quiz - Quiz

How do divisibility rules apply when the expressions involve variables instead of plain numbers? In this quiz, you’ll explore how to test algebraic expressions for divisibility by analyzing factors, rewriting terms, and applying familiar rules in symbolic form. You’ll practice identifying multiples, checking remainders, and using structure to determine whethe... see morean expression satisfies a divisibility condition. Step by step, you’ll strengthen your ability to reason about number properties within algebraic expressions.
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2) Which equation represents numbers that leave a remainder of 2 when divided by 5?

Explanation

Dividing by 5 leaves remainder 2 ⇒ n = 5k + 2.

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3) If n = 6k, then n is divisible by both 2 and 3.

Explanation

6k = 2×3×k, showing divisibility by both 2 and 3.

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4) Which algebraic form shows all even numbers?

Explanation

Even numbers are multiples of 2, so x = 2n for some integer n.

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5) A number divided by 7 leaves a remainder of 4. The equation is: ____

Explanation

General form for numbers leaving remainder 4 when divided by 7 is n = 7k + 4.

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6) Which equation models all numbers divisible by both 2 and 5?

Explanation

LCM(2,5) = 10, so x = 10n represents numbers divisible by both.

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7) A number is divisible by 12 if it is divisible by:

Explanation

12 = 3×4, so divisibility by both 3 and 4 ensures divisibility by 12.

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8) Which algebraic form shows all odd numbers?

Explanation

Odd numbers can be written as 2k + 1.

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9) Which number satisfies both: divisible by 6 and leaves remainder 2 when divided by 5?

Explanation

42 ÷ 6 = 7 (divisible); 42 ÷ 5 leaves remainder 2.

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10) If a number is divisible by 9, it must also be divisible by 3.

Explanation

Since 9 = 3×3, divisibility by 9 implies divisibility by 3.

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11) Which number is divisible by 3 but not by 9?

Explanation

24 ÷ 3 = 8 (divisible), 24 ÷ 9 ≠ integer (not divisible by 9).

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12) A number divided by 8 leaves remainder 3. The general form is: ____

Explanation

The remainder form is n = 8k + r, so n = 8k + 3.

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13) Which number satisfies: divisible by 4 and leaves remainder 1 when divided by 3?

Explanation

To leave remainder 1 when divided by 3, we write n = 3k + 1.

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14) Which equation represents numbers divisible by both 3 and 5?

Explanation

LCM(3,5) = 15, so x = 15n models such numbers.

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15) All numbers of the form n = 10k + 5 are divisible by 5.

Explanation

10k is divisible by 5, so 10k + 5 is also divisible by 5.

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16) Which value of x makes 5x + 2 divisible by 3?

Explanation

Substitute values: 5(2)+2=12, which is divisible by 3.

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17) Find x such that 7x + 2 is divisible by 3.

Explanation

7(1)+2=9, which is divisible by 3.

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18) If a number is divisible by both 2 and 3, then it can be written as ____

Explanation

LCM(2,3)=6 ⇒ n = 6k represents all such numbers.

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19) Select all correct divisibility rules.

Explanation

Rules: 2→last digit even; 3→digit sum multiple of 3; 9→digit sum multiple of 9; 10→ends in 0.

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20) If n = 9k + 1, what is the remainder when n is divided by 9?

Explanation

n = 9k + 1 means dividing by 9 leaves remainder 1.

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A number n is divisible by 4. Which equation represents this?
Which equation represents numbers that leave a remainder of 2 when...
If n = 6k, then n is divisible by both 2 and 3.
Which algebraic form shows all even numbers?
A number divided by 7 leaves a remainder of 4. The equation is: ____
Which equation models all numbers divisible by both 2 and 5?
A number is divisible by 12 if it is divisible by:
Which algebraic form shows all odd numbers?
Which number satisfies both: divisible by 6 and leaves remainder 2...
If a number is divisible by 9, it must also be divisible by 3.
Which number is divisible by 3 but not by 9?
A number divided by 8 leaves remainder 3. The general form is: ____
Which number satisfies: divisible by 4 and leaves remainder 1 when...
Which equation represents numbers divisible by both 3 and 5?
All numbers of the form n = 10k + 5 are divisible by 5.
Which value of x makes 5x + 2 divisible by 3?
Find x such that 7x + 2 is divisible by 3.
If a number is divisible by both 2 and 3, then it can be written as...
Select all correct divisibility rules.
If n = 9k + 1, what is the remainder when n is divided by 9?
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