Coprime Numbers in Algebraic Contexts

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1) Solve for x: GCD(7, x) = 1. Which x works?

Explanation

7 is prime; 20 = 2² × 5 → no shared factors → coprime.

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About This Quiz
Coprime Numbers In Algebraic Contexts - Quiz

Once you know how to spot coprime numbers, it’s time to use them in equations. In this quiz, you’ll solve problems where GCD rules help determine possible values of variables, explore linear equations like ax + by = 1, and connect coprimes to fractions in simplest form. We bring you... see morethis quiz to show how number theory meets algebra. see less

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2) If a and b are coprime, then ax + by = 1 has:

Explanation

That’s a key result in number theory (Bezout’s Identity).

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3) Which of these pairs is coprime?

Explanation

11 = prime; 28 = 2² × 7 → no shared factors → coprime.

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4) Solve: If GCD(15, x) = 1, which value of x works?

Explanation

15 = 3 × 5; 22 = 2 × 11 → no overlap → coprime.

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5) If (a, b) = 1, what is always true?

Explanation

If (a, b) = 1 → there exist integers x, y with ax + by = 1.

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6) Which pair is not coprime?

Explanation

Both share 3’s as factors.

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7) If GCD(25, x) = 1, which x works?

Explanation

25 = 5²; 14 = 2 × 7 → no common factor → coprime.

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8) Which of these pairs are coprime?

Explanation

(4,9), (8,15), and (11,28) have no shared factors.

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9) Which pair is coprime?

Explanation

17 is prime; 24 = 2³ × 3 → no overlap → coprime.

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10) If a and b are coprime, what is LCM(a, b)?

Explanation

They have no shared primes, so LCM equals their product.

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11) Solve: GCD(18, x) = 1. Which x works?

Explanation

18 = 2 × 3²; 11 is prime and unrelated → coprime.

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12) If GCD(a, b) = 1, which of these equations has integer solutions?

Explanation

If GCD(a, b) = 1 → ax + by = 1 has integer solutions.

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13) Which pair is coprime?

Explanation

13 = prime; 20 = 2² × 5 → no shared factors → coprime.

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14) Which statement is true?

Explanation

All distinct primes are coprime.

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15) Solve: If GCD(21, x) = 1, which value of x works?

Explanation

21 = 3 × 7; 20 = 2² × 5 → no overlap → coprime.

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16) Which of these pairs is not coprime?

Explanation

Both share factor 4 → not coprime.

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17) If a and b are coprime, then GCD(a², b²) = ?

Explanation

Their squares don’t add shared factors.

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18) Which pair is coprime?

Explanation

29 = prime; 40 = 2³ × 5 → no common factors → coprime.

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19) If GCD(a, b) = 1, what is always true about fractions a/b?

Explanation

No further reduction is possible because they share no common divisor.

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20) If GCD(12, x) = 1, which x values make (12, x) coprime?

Explanation

12 = 2² × 3; 11 is prime and doesn’t share 2 or 3 → coprime.

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Solve for x: GCD(7, x) = 1. Which x works?
If a and b are coprime, then ax + by = 1 has:
Which of these pairs is coprime?
Solve: If GCD(15, x) = 1, which value of x works?
If (a, b) = 1, what is always true?
Which pair is not coprime?
If GCD(25, x) = 1, which x works?
Which of these pairs are coprime?
Which pair is coprime?
If a and b are coprime, what is LCM(a, b)?
Solve: GCD(18, x) = 1. Which x works?
If GCD(a, b) = 1, which of these equations has integer solutions?
Which pair is coprime?
Which statement is true?
Solve: If GCD(21, x) = 1, which value of x works?
Which of these pairs is not coprime?
If a and b are coprime, then GCD(a², b²) = ?
Which pair is coprime?
If GCD(a, b) = 1, what is always true about fractions a/b?
If GCD(12, x) = 1, which x values make (12, x) coprime?
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