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 sum of the squares of two consecutive integers is 145. What are the integers?

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If the radius of a circle is 7 cm, what is its circumference?

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What is the greatest common divisor (GCD) of 36 and 48?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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