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### Course: Class 7>Unit 2

Lesson 2: Finding HCF

# Greatest common factor examples

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators. Created by Sal Khan.

## Want to join the conversation?

• Why does multiplying the common prime factors work to show the greatest common divisor? How come there is no greater number besides the answer?
• for example the question is gcd(8,24)
8 = 2*2*2
24 = 2*2*2*3
there are 3 two in both 8 and 24. so lets simplify all the common factors:
2*2*2 = 2*2*2
8=8
gcd = 8
• The GCF (or GCD) is very useful in simplifying complex math problems when you move on to more advanced material. Sometimes, it can make the difference between being able to solve the problem and not being able to solve them.

For this level of math, it helps you reduce fractions to their simplest form, thus helping you to better understand the numbers involved. For example, would you realize, without simplifying that 226/791 is the same thing as 2/7?

so if you are dealing with fractions... also this is the base of many other (used in life) advanced math problems.

so fractions and it is the basis of many other advanced math problems you will use more in life.
• Yes, there is the difference between GCF and GCD is that GCF is the greatest common factor and GCD is the greatest common denominator. A factor is a number or quantity that when multiplied with another produces a given number or expression. A denominator is the number below the line in a common fraction; a divisor.
I hope this helps!:)
• can't you just think of 7 as a prime number and apply the gcd as 1? is 1 the only factor other than the number itself for every prime number? does prime factorization work for every gcd?
• Prime definition is whole number which is not divisible by any other whole number except itself and 1, so yes to the second question. 1st question is yes as long as the other number is not a factor of 7. and yes prime factorization will always work to see what is common between two numbers.
It helps to learn divisibility rules
All even numbers (except 2) has 2 as a factor
If the last two digits (tens and ones) are divisible by 4, whole number is divisible by 4 (or divide by 2 twice)
If the last 3 digits (hundreds, tens and ones) are divisible by 8, whole number is divisible by 8 (or 2 three times).
If the sum of the digits add up to a factor of 3, it is divisible by 3, and same thing if add up to 9, divisible by 9 (or 3 twice)
6 is a combo of 2 and 3.
If the ones digit is 5 or 0, it is divisible by 5.
With any zeroes on end, you have equal number of 5s and 2s
This covers all numbers up to 10 except 7.
• Because a lot of people do not get it, I will expand apon the idea.

GCF is saying that what number can go into __ and ___ ?

For example, let’s take 24 and 36

So we write out the factors:

24: 1,2,12,24
36:1,3,12,36

Now we find what they both have in common? Try and figure it out yourself.

Did you get it? It’s 12. So 12 is our GCF or GCD
• yes but you for got you have to have the greatest common factor you said just a common factor
• Around why did Sal chose 3 over the 2? Two is the smallest number that goes into 21.
• well actually. since two is an even number, it cannot add up to an odd number so in this case three was actually the smallest number
• Is the greatest common divisor another name for the greatest common factor??
• Good question! This question confused me for a bit too. Anyway, Yes, it is.