The GCF or the greatest common factor is also known as the HCF or the highest common factor. This refers to the biggest positive integer of two or more integers which can divide the numbers without getting a remainder. In other words, it’s the highest number which divides into two or more numbers exactly. Using this GCF calculator, you can easily come up with the greatest common factor without having to compute manually.
How to use the GCF calculator?
This greatest common factor calculator will automatically generate the GCF for two or more numbers of your choice. To use it, you need one simple step:
- To use this common factors calculator, just input the numbers.
- After that, the tool will automatically generate the greatest common factor of the numbers.
- Also, the greatest common divisor calculator will give you the individual factors of the numbers you’ve entered.
What is the greatest common factor?
The greatest common factor is also known as GCF, GCD or HCF. It refers to the largest positive integer which evenly divides into a whole set of numbers without a remainder. For instance, for the numbers 42, 30, and 18, the greatest common factor is 6.
There are different ways to find the GCF if you don’t want to use the GCF calculator. The best method to use would depend on how many numbers that you have, how large those numbers are, and what you plan to do with the GCF you acquire.
If you want to find the GCF through factoring, you should list down all the factors of each number in the set. Either that or you can use a factors calculator to find them. The factors refer to the numbers which divide into the main number evenly with zero as the remainder. Then compare the factors for each of the numbers in your set and the largest common number us the GCF.
This method is similar to factoring, but it has a slight difference. To find the GCF, first list all the prime factors of each of the numbers in your set. Then make a list of all the prime factors which appear in all of the original numbers. Make sure to include the highest number of occurrences of each of the prime numbers. Finally, multiply these numbers together to compute for the GCF. This method is ideal for larger numbers compared to straight factoring.
So, what should you do if you need to find the GCF of a set of very large numbers such as 137,688 and 154,875? If you have a greatest common factor calculator, then this would be a breeze. But if you need to work by hand, finding the GCF would take a lot of time. That is unless you use Euclid’s Algorithm. Here’s how:
- Start with two whole numbers and subtract the smaller one from the larger one. Take note of the result.
- Keep on subtracting the smaller number from the result that you get until you get a number that’s smaller than your original small number.
- Then make use of the original small number as the new large number. Subtract the result from the previous step from your new large number.
- Keep repeating the steps each time you get a new large number and a new small number until you get zero as a result.
- Check the number that you’ve acquired before reaching zero. This is the GCF.
How do you calculate the greatest common factor?
To demonstrate this, let’s start with a set of numbers. Let’s say we want to get the GCF of 72, 54, and 42.
- First, list the prime factorization of each of the numbers:
72 = 2 * 2 * 2 * 3 * 3
54 = 2 * 3 * 3 * 3
42 = 2 * 3 * 7
- Then search for the factors which each of the numbers have in common. In this example, the factors are 2 and 3.
- For each factor, get the highest factor which is still 2 and 3.
- Then multiply these factors to get 6 as the GCF.
- If you want, you can check your result using the online calculator.
As you can see, this method is easy as long as you know how to get the prime factorization of each of the numbers. If you think doing this is too much, then you can use an online calculator to generate the numbers for you.
One concept that’s closely related to GCF is the LCM or least common multiple. You can find the LCM using a similar process as finding the greatest common factor. When you can break the numbers down to their prime factorization, this time, you look for the smallest power of each of the factors instead of the largest power. Just like with the GCF, you can compute this by hand or use an LCM calculator which is a lot easier. Let’s see another example for the set of numbers 2, 3, and 7:
- For the prime factorization:
2 = 2 * 2 * 2
3 = 3 * 3 * 3
7 = 7
- This means that the LCM is 2 * 2 * 2 * 3 * 3 * 3 * 7 = 1512
What is an example of a common factor?
Knowing how to calculate the GCF is important. But it’s also very helpful to learn the common factors of certain numbers. Here are some examples for you:
- Factors of 8: 1, 2, 4, 8
- Factors of 75: 1, 3, 5, 15, 25, 75
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 6: 1, 2, 3, 6
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 20: 1, 2, 4, 5, 10, 20