HCF of 3 Numbers Calculator

The abbreviation of HCF is Highest common factor and it is the highest integer that exactly divisible by all given numbers with remainder zero. The denotation for HCF of three numbers like a, b, c is HCF(a, b, c).

How to Find HCF of 3 Numbers Easily?

For finding the highest common factor of three numbers, we have various major approaches which can make your calculations so easy and quick. The list of methods that are used to find the HCF of 3 numbers are given here along with detailed steps and solved examples. Take a look at all the methods of finding the Highest common factor of 3 numbers and use the apt method that fits for your given input integers.

• Factoring
• Prime Factorization
• Division Method

Detailed Steps for Finding HCF of Three Numbers Using Factoring Method

• In the initial step, find out the list of all factors for each number to solve the Highest common factor.
• These factors divide the given numbers evenly with zero remainders.
• Later, list out the common factors and consider the largest common factor as HCF of three numbers.

Example:

Find the HCF of 80, 45, 32 using Factoring?

Solution:

Given numbers are 80, 45, 32 and find the factors for each number initially,

The factors of 32 are 1, 2, 4, 8, 16, 32

The factors of 45 are 1, 3, 5, 9, 15, 45

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Now, list the common factors from each number, there is only one common factor for all three numbers ie., 1.

Thus, HCF(80, 45, 32) is 1.

Highest Common Factor of 3 Numbers by Prime Factorization Method

The steps that are involved in finding the highest common factor of three numbers using prime factorization are listed here:

• First and foremost, you need to find the prime factors of each of the three numbers.
• Later, identify the common prime factors of the 3 numbers
• Next, multiply the highest occurrence of common factors.
• Finally, the result of the common factors multiplication is the Highest Common Factor of the three numbers.

Example:

Find HCF(36, 27, 80) by Prime Factorization?

Solution:

Given three numbers to find HCF are 36, 27, and 80

Step 1: Find the product of prime factors for each given number.

Prime factors of 36 = 2² × 3²

Prime factors of 27 = 3³

Prime factors of 80 = 2⁴ × 5

Step 2: HCF is the product of all common prime factors using the least power of each common prime factor. Here there are no common prime factors for the given numbers.

So, the answer for HCF of three numbers 36, 27, and 80 is 1.

Procedure on HCF of 3 Numbers using Division Method

A Division Method is also one of the best methods to solve the Highest common factor of three numbers. For three numbers, first, we need to calculate the HCF using the division method for two numbers then again HCF of two numbers result and the third number. The steps to find out HCF of two given numbers using the division method are as follows:

• Initially, take a large number as a dividend and a small number as a divisor.
• Now, Divide the larger number by the smaller number.
• If the remainder is not zero then the divisor of step 1 is divided by its remainder.
• Repeat the process till we get the zero as the remainder.
• Finally, the last divisor is the HCF of two numbers.
• Now, find out the HCF of two numbers and left third numbers using the division method to get the result for HCF of given three numbers.
• Take the HCF of two numbers result and third number and repeat the process as we did for finding the HCF of two numbers
• The final divisor after calculating the whole process is considered as the Highest common factor of three numbers.

Example:

Find the HCF of 9, 27, and 48 using the division method?

Solution:

Given three numbers are 9, 27, 48

Now take two numbers first for finding the HCF of two numbers

Let's first, find out HCF of 9 and 27 by division method,

Thus, HCF of 9 and 27 = 9

Now, find out HCF of 9, 27, and 48

⇒ HCF of [(HCF of 9, 27) and 48]

⇒ HCF of (9, 48)

Apply the division method steps and find out the HCF of 9 and 48

So, the answer for HCF of 9, 27, 48 is 3.

How to Find Factors of a Number?

Factors of a given number are an integer that divides the given number completely with no remainders.

We can find factors by different methods. One of them is to divide the original number starting from the smallest number, i.e. ‘2’. Here, divisors whose remainder is zero are the factors of the original number. Also, the quotients of all the divisors are also the factors of the original number.

What are GCD, HCF, and GCF? 

The Greatest Common Divisor (GCD) of a given set of numbers is the greatest factor when we divide the given set of numbers by it, we get the whole number quotient with no remainder every time. The Greatest Common Factor (GCF) of a set of numbers is a number which is a common factor to all the given numbers. The Highest Common Factor (HCF) is the same as GCF & GCD.

HCF of 3 Numbers Formula

Here is a formula to calculate the HCF of 2 or more fractions:

HCF (fractions) = HCF (all no in numerator) / LCM (all no in denominator)

Solve for Highest Common Factor of 3 Numbers with Steps

Here are the steps to calculate the HCF of 3 numbers using prime factorization:

1. Check all the 3 numbers to calculate the HCF & select any 2 numbers out of 3 numbers.
2. Find prime factors of these 2 numbers.
3. Select common factors among the factors of the 2 numbers
4. Multiply them to get the HCF of 2 numbers.
5. Now, find the prime factors of the 3rd number & the HCF of 2 numbers.
6. Find the common factors between them.
7. Multiply these factors to get the HCF, which is the HCF of all 3 numbers.

Easy Way to Find HCF of 3 Numbers: Solved Example

Example: 

Find the HCF of 36, 80 & 46.

Solution:

Here, the numbers are 36, 80 & 46.

Let us first take 36 & 80. & find their prime factors.

Prime factors of 36 are 2, 2, 3, 3.

Prime factors of 80 are 2, 2, 2, 2, 5.

Here, common factors among the above factors are 2 & 2.

So now the HCF (36, 80) = 2 x 2 = 4

Now we will find the prime factors of 46 & HCF

Prime factors of 46 are 2, 23.

Prime factors of 4 are 2, 2.

Now the common factor among the above factors is 2.

So, now we can say that the HCF of numbers 36, 80 & 46 is ‘2’.

FAQs on Online HCF calculator- Highest Common Factor

• How do you find the HCF of 3 numbers by division?

To find out HCF by division method, consider the smaller number among the 3 numbers, as the divisor and consider the second smaller number as the dividend, now begin with the division process until the remainder is 0.

• What is the HCF of 136 170 and 255?

Determining HCF is easy as 17 is the largest common factor shared by the given three numbers. Hence 17 is the HCF for the above-given numbers.

• What is LCM and HCF calculator?

LCM and HCF calculator is an online tool specially designed to determine the LCM and HCF values for multiple numbers at a single place. You can find out several tools at hcflcm.com to understand more such mathematical concepts in no time.

• How do I find the HCF of 3 numbers online?

First, enter the three numbers in the input space given, then click on the "Calculate" button, and scroll down to check the results with an explanation. To enter the next set of numbers press the "Reset" button.