Topic Details (Notes format)

How to Find the Greatest Common Divisor (GCD)

Subject: Mathematics

Book: Maths Mastery

Also known as the Greatest Common Factor (GCF), the GCD of two numbers is the largest positive integer that divides them both without leaving a remainder. The standard method is the Euclidean Algorithm: if you want the GCD of 48 and 18, for instance, repeatedly apply gcd(a, b) = gcd(b, a mod b). With 48 and 18, 48 mod 18 = 12, so gcd(48, 18) = gcd(18, 12). Next, gcd(18, 12) = gcd(12, 6), and finally gcd(12, 6) = 6. So the GCD is 6. GCD calculations apply to simplifying fractions, finding common denominators, cryptography, and more. Mastering the Euclidean Algorithm also fosters efficiency in many integer-based math problems.

Practice Questions

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If 2x - 3 = 7, what is the value of x?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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What is the sum of all angles in a hexagon?

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If 2x = 16, what is the value of x?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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