Finding the Greatest Common Factor

Luis and June seem to be struggling to find some common factors between them. Speaking of common factors, let's learn about finding the greatest common factor. The Greatest Common Factor, or GCF, is the largest number that divides equally into two or more numbers. We often use the GCF to solve problems involving equal sharing, like dividing a cake or distributing supplies between your friends. There are two methods of finding the GCF; factor pairs and factor trees. First, let's explore factor pairs. This method lists out factor pairs and is most useful for smaller numbers. For this strategy, we will use twelve and fifteen. Factor pairs for twelve are one and twelve, two and six, and three and four. Factor pairs for fifteen are one and fifteen, and three and five. Now find the largest factor that both numbers have in common. What is the highest factor twelve and fifteen have in common? Three, so the GCF of twelve and fifteen is three. Now let's explore the second method, factor trees which uses prime factorization. This method is most useful when dealing with larger numbers. First, start with the numbers at the top; here we have twenty-four and thirty-six. Now find the prime factorization for each number. For twenty-four, we have two and twelve, two and six, and two and three. For thirty-six, we have two and eighteen, two and nine, and three and three. Next, identify the shared prime factors. Both twenty-four and thirty-six share a two, another two, and a three. Finally, multiply these together to find the GCF. We need to solve two times two times three. Two times two equals four, and four times three equals twelve. The GCF of twenty-four and thirty-six is twelve. Now it's your turn! Find the GCF of thirty-six and fifty-four. Pause the video to work on the problem, and press play when you are ready for the solution. The factor tree of thirty-six is four and nine, two and two, and three and three. The factor tree of fifty-four is six and nine, two and three, and three and three. The shared factors are a two, a three, and another three. Multiplied together you get a GCF of eighteen. Let's summarize. There are two useful methods for finding the greatest common factor, or GCF. The first method is factor pairs. This is useful for finding the GCF with smaller numbers. The second method is factor trees. This is useful for finding the GCF with larger numbers. Finding the GCF can help in making fair and efficient decisions when it comes to sharing. Ah, it looks like Luis and June have finally found their greatest common factor, their love for math and factor trees!