When do i use gcf

The greatest common factor, then, can be found when you list out the factors of each number and then find the greatest one that is in common in between the two. Let's take a quick example: finding the greatest common factor between 9 and Let's start by factoring. Factoring is the process of finding the factors of a number.

Which is the largest number in common between the two lists? We can see that 3 is both a factor of 9 and It is the largest factor they have in common, so we can name 3 as the GCF or greatest common factor. A multiple is a larger number the number can be divided into without leaving a remainder. For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on.

The LCM, then, is the smallest number in common when you list the multiples of two or more numbers. We use greatest common factors all the time with fractions, and as fractions are used a lot in everyday life, this makes GCF very useful! By finding the GCF of the denominator and numerator, you can then successfully simplify a fraction or ratio.

Then we divide both parts by the HCF to simplify. It also works for ratios, where you can simplify each side using HCF to find out a 1:X ratio.

This can be useful if you are using a ratio for a recipe or order as you can use one piece of information to find out the right ratio for any combination. So, to put this into a situation, say you know that for every 5 people at a party, you need 15 sandwiches. The HCF of these two numbers is 5, so for each person you need:. So, if we want to give cakes to all our friends, and need 25 cupcakes what a popular mathematician!

For higher grades, when dealing with students with anxiety over algebraic manipulations and fractions operations, it is also useful to identify if procedural fluency of finding GCF and LCM might be the root cause.

Your email address will not be published. Fractions GCF is most commonly used when reducing a fraction to its lowest terms, while LCM is used when adding unlike fractions. One piece is 72 inches wide, and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? Bennie is catering a party and putting snack food on plates. He has 72 cheese puffs and 48 carrot sticks.