GCF

GCF or Greatest Common Factor is the highest number that can divide exactly into a set of numbers. (For example: 7 is the GCF of 14 and 49, 7 divide into 14 twice and divides into 49 seven times.)

Some numbers are easy enough to do the math mentally (For example: 3 and 9, you can quickly see that the highest factor that goes into both those numbers is 3), but when there are higher numbers or more than a set of two numbers, you can use prime factorization in order to help you find the GCF.

The First Step

Find the prime factorization of the given numbers. (Prime Factorization – Prime factors of a number, the sum is equal to the number)

The Second Step

Find the prime factors in common, also choose the smallest exponent between the common prime factors. 

The Last Step

Multiply all the common factors and the smallest exponents in order to find the GCF. 

(The same steps no matter how high the numbers or how many numbers you are working with.)

LCM

LCM or Lowest Common Multiple is the lowest number that is a multiple of a set of numbers. (For Example: 12 is the lowest common multiple of 2, 3, and 4.)

Again, for finding LCM, you could probably do the math mentally when the numbers are small like 2, 3, and 4. But for higher numbers, instead of listing out all the multiples of each number and finding which is the lowest multiple in common, we can use prime factorization.

The First Step

Find the prime factors of each number.

The Last Step

Take all the prime factors and their highest exponent. Multiply to find the LCM.

This week, we learned about prime factors, prime factorization, and how to apply prime factorization when trying to find the GCF and LCM. One challenge with this lesson is that there is a lot of mental math and math without a calculator. You need to figure out a lot when it comes to factors especially, like doing the math on whether a number divides exactly into another number when trying to find the prime factors. It is a very good thing to learn because it trains our minds and helps us learn how to do math without a calculator.