# Lesson 92 – Doodles Do Algebra

Today your child begins learning about the greatest common divisor. This is the largest shared combination of prime factors that make up two expressions.

As an example, the greatest common divisor between 6ab and $15a^2c$ is 3a. For more complicated expressions, you simply find all the prime factors of each expression and then select all those in common between both expressions.

1. Step One is find the prime factors. So prime factors of $4a^2x^3$ are 2, 2, a, a, x, x, x. And the prime factors of $10ax^3$ are 2, 5, a, x, x, x. Comparing the two, the common primes are 2, a, x, x, x so the greatest common divisor is $2*a*x*x*x=2ax^3$
2. Prime factors of $9abc^3$ are 3, 3, a, b, c, c, c and prime factors of $12bc^4x$ are 2, 2, 3, b, c, c, c, c. So comparing the two, the common primes are 3, b, c, c, c and the greatest common divisor is $3bc^3$
3. Prime factors of $3a^4y^3$ are 3, a, a, a, a, y, y, y. Prime factors of $6a^5x^3y^5$ are 2, 3, a, a, a, a, a, x, x, x, y, y, y, y, y. Prime factors of $9a^5y^4z$ are 3, 3, a, a, a, a, a, y, y, y, y, z. So comparing the three expressions, the common primes are 3, a, a, a, a, y, y, y and the greatest common divisor is $3a^4y^3$.
4. Prime factors of $4a^3b^2x^5y^3$ are 2, 2, a, a, a, b, b, x, x, x, x, x, y, y, y. Prime factors of $8a^5x^3y^3$ are 2, 2, 2, a, a, a, a, a, x, x, x, y, y, y. So comparing the two expressions, the common primes are 2, 2, a, a, a, x, x, x, y, y, y and the greatest common divisor is $4a^3x^3y^3$.
5. $4x^3$
6. $3a^3y^3$