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

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

View Question

If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

View Question

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

View Question

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

View Question

The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

View Question

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

View Question

If x = 3 and y = 4, what is the value of x^2 + y^2?

View Question

If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

View Question

If the probability of an event is 1/4, what is the probability of its complement?

View Question

How many diagonals does a pentagon have?

View Question