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 area of an equilateral triangle with side length 6 cm is:

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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A cube has a side length of 4 cm. What is its volume?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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What is the remainder when 5^100 is divided by 3?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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If 5x - 2 = 13, what is the value of x?

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