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

A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

View Question

A car travels 240 km in 4 hours. What is its average speed?

View Question

What is the square root of 144?

View Question

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

View Question

If x² - 9x + 18 = 0, what are the roots of the equation?

View Question

A sum triples in 20 years at simple interest. What is the rate of interest per annum?

View Question

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

View Question

A train 150 m long passes a pole in 15 seconds. What is its speed?

View Question

A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

View Question

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

View Question