The highest common factors explained for primary students

What is the highest common factor?

The highest common factor is the greatest common factor and abbreviated as “HCF” or “GCF.” We can calculate it manually or by using an HCF calculator. HCF can be explained as a combination of the following terms:

 A Factor:

Factors are all those numbers that are multiplied to get another number. For example, if we take any two numbers, such as 6 and 3, and multiply them, we will get another 18. We can write it as:

• 6×3=18
• 9×2=18

In the examples mentioned above, it can be observed that the number 18 has four possible factors in two different equations. Therefore, we can conclude that the factors of number 18 are:

• 1
• 6
• 3
• 9
• 2
• 18

These numbers can be multiplied in different combinations to get the number 18 as a final result.

A common factor

Now the second term to explain the highest common factor is the common factor. A common factor can be defined as a factor that numerous numbers will share. For instance, take the number 7 as an example.

Seven will be shared by a common factor of 14 and 21 simultaneously.

• Common factors of 14 are: 7 and 2 (7×2=14)
• Common factors of 21 are: 7 and 3 (7×3=21)

So it is proved that number 7 is present as the factors of both numbers that’s why we call it common factor.

In the same way, two will serve as a common factor of number 8 and number 12 simultaneously.

Highest common factor

Now the highest common factor can be explained as a combination of factor and common factor. We can define it as the highest whole number that is shared by multiple numbers.

• Let’s take the example of 10. The factors of 10 are 2, 5, and 10.
• Now let’s look at the factors of 20: 2, 5, 10, and 20.
• Now identify the common factor of these two numbers: 2, 5, and 10.
• The highest factor that is common among the factors of these two numbers is: 10
• So the highest common factor for number 10 and 20 is: 20

Relationship of highest common factors with other areas of mathematics

The highest common factor can be used in the following practice of mathematics:

1. The highest common factors are valuable for simplifying the complex and large fractions.
2. They are helpful for the comparison of fractions.
3. It can spill numbers into two smaller portions.
4. It can equally distribute two or more sets into their largest grouping.
5. A fraction can be expressed in its simplest form by finding the numerator’s highest common factor or a top number and the denominator or bottom number. For example:

We have an equation that is 18 / 24.

• Find the highest common factor of 18 and 24.
• Factors of 18 = 18, 9, 6, 2, 3
• Factor of 24 = 24, 2, 6, 12, 3
• Highest common factor is = 6
• Now divide the equation by number 6 = 18 / 24 = 3 / 4.

How can we find the highest common factor?

Several methods and tools can calculate the highest common factors. Some of them are explained below:

Factorization method

The factorization method to figure out the HCF of 12 and 16 is explained as follows:

Factorization uses all the possible factors of given numbers to figure out the highest common factor. It has the following steps:

• First of all, List all the possible factors of the required numbers.
• Highlight all the common factors.
• Filter out the common greatest factor.

Division Method

The division method is another approach to calculate the HCF. It can have applied as:

• Divide the present highest number by the minimum number.
• Now Take out the divisor from the previous step.
• Divide the divisor with the remainder you got in the first step.

Keep repeating the 2nd and 3rd steps until the remainder becomes zero. In the end, The preceding divisor will be the highest (greatest) common factor.

Example:

To understand this approach, have a look at the following example:

If the given numbers are 30 and 42. Follow the steps mentioned above:

• 42 / 30 = dividing by 30 gives the reminder = 12
• Now 30 / 12 gives the reminder = 6
• Now divide 12 / 6 gives the reminder = 0
• So the highest common factor is six as it gives no reminder.

Prime Factorization

You can find the HCF by implementing the method of prime factorization. It has the following steps:

• You have to make the factors of a number by using a factor tree.
• Now encircle the common factors.
• Multiply all the common factors to get the highest common factor.
• Sometimes there will be only one common factor. In such situations, there is no need to multiply. This only common factor will be the highest common factor.

For example:

Take two numbers. In this example, we are taking 24 and 36. Make their factors.

Number 24

• Factors of 24 are 2 and 12
• Factors of 12 are 6 and 2
• Factors of 6 are 2 and 3

Number 36

• Factors of 36 are 2 and 18
• Factors of 18 are 2 and 9
• Factors of 9 are 3 and 3

Now find the common ones: 2, 2, and 3.

Multiply all the common factors: 2x2x3 =12

So, the HCF = 12

AllMath

This tool finds out the highest common factors of all the given numbers in the blink of an eye.

1. All you need to do is to enter the number in the given space.
2. Select the method from which you want to calculate the highest common factors.
3. You can check the highest common factor in the following ways:
   • List of factors
   • Division steps
   • Prime factorization
   • Upside down division
   • Euclidean algo
   • Binary algo
4. The tool is free to use and easily accessible online.
5. You can make unlimited calculations within no time.

Mera Calculator

This Calculator lets you Enter up to 10 numbers for the calculation of Greatest Common in steps. GCF, GCD, and HCF are some terms to represent one concept.

GCF calculators use the following approaches to calculate GCF.

1. List of Factors Method
2. Prime Factorization Method
3. Division Method
4. Euclidean Algorithm
5. Binary (Stein’s) Algorithm
6. Upside Down Division

Calculator Soup

1. Enter whole numbers that commas or spaces must separate.
2. GCF will be displayed for the given numbers by a prime factorization method.
3. You can use it without paying any money
4. It allows you to make an unlimited calculation as well
5. This Calculator gives you the solution for finding:
   • Greatest common factor (GCF)
   • The greatest common denominator (GCD)
   • Highest common factor (HCF)
   • Greatest common divisor (GCD)

Conclusion

Finding the factors, common factors, and greatest common factors might be difficult and time-consuming in many cases. For the ease of calculations and to save time, take help from some tools. They will give you results in a fraction of seconds. Furthermore, the risk of all the possible errors will be eliminated as well. The manual calculation is also capable of giving you the most precise results if handled carefully!