Lesson 92 – Doodles Do Algebra

lesson92doodlepoodlecToday 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.

Download

Answers:

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

 doodlemom