**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

**HCF Using Euclid’s Division Lemma Method:** Finding the Highest Common Factor by Euclid’s Division Lemma Algorithm is a standard approach by all the students. Here, we will see the detailed process on How to Find HCF of two or more numbers by Euclid’s Division Lemma Algorithm.

The Highest Common Factor (HCF) Calculator is used to calculate GCF of two or more whole numbers. Here, you can enter numbers separated by a comma “,” and then press the Calculate button to get the HCF of those numbers using the Euclidean division algorithm.

**Ex: **HCF of 24, 48, 64 (or) HCF of 16, 56, 12 (or) HCF of 8, 72, 48

**Here are some samples of HCF Using Euclids Division Algorithm calculations.**

Related Calculators:

- LCM of two Numbers Calculator
- GCF of two Numbers Calculator
- LCM of two or more Numbers Calculator
- GCF of two or more Numbers Calculator

The basis of the Euclidean division algorithm is Euclid’s division lemma. Euclid’s division algorithm is a method to calculate the Highest Common Factor (HCF) of two or three given positive numbers. Euclid’s Division Lemma says that for any two positive integers suppose a and b there exist two novel whole numbers say q and r, such that, **a = bq+r, where 0≤r**

Here, a and b are given numbers whereas q and r are Quotient and Reminder.

To find the Highest Common Factor (HCF) of two positive integers a and b we use Euclid’s division algorithm. Highest Common Factor (HCF) of two or more numbers is the greatest common factor of the given set of numbers. If we consider two numbers to find the HCF using Euclid’s Division Lemma Algorithm then we need to choose the largest integer first to satisfy the statement, a = bq+r where 0 ≤ r ≤ b.

Let’s get deep to see how the algorithm works when finding the HCF of two or more given numbers.

Follow the below steps to find the HCF of given numbers with Euclid’s Division Lemma:

**Step 1:** Apply Euclid’s division lemma, to a and b. So, we find whole numbers, q and r such that a = bq + r, 0 ≤ r < b.

**Step 2: **If r = 0, b is the HCF of a and b. If r ≠ 0, apply the division lemma to b and r.

**Step 3:** Continue the process until the remainder is zero. The divisor at this stage will be the required HCF of a and b.

Thus, Euclid’s Division Lemma algorithm works because HCF (a, b) = HCF (b, r) where the symbol HCF (a, b) denotes the HCF of a and b,

*Example: Use Euclid’s algorithm to find the HCF of 36 and 96.*

**Solution:**

Given HCF of two numbers ie., 36 and 96. The larger number from both a and b is 96, hence, apply the Euclid Division Lemma algorithm equation a = bq + r where 0 ≤ r ≤ b.

We have a= 96 and b= 36

⇒ 96 = 36 × 2 + 24, where 24≠0.

So, again apply the Euclid’s Division Algorithm for new dividend as 36 and divisor as 24

⇒ 36 = 24×1 +12, where 12≠0

Again take dividend as 24 and divisor as 12.

⇒ 24 = 12×2 +0, here reminder=0

As the remainder becomes zero, we can halt the process here itself. As per the Euclid’s division Lemma algorithm, the last divisor is 12.

Thus, the HCF of 36 and 96 is** 12.**

Explore completely about HCF using Euclid’s Division Lemma Concept from our website lcmgcf.com provided calculator and make your calculations easier & faster.

- HCF of 16, 32, 40
- HCF of 272, 1032
- HCF of 662, 970, 684
- HCF of 60, 132, 360
- HCF of 240, 200
- HCF of 8925, 7399
- HCF of 25, 37
- HCF of 15, 25, 30
- HCF of 91, 112, 49
- HCF of 15, 60, 120
- HCF of 391, 425, 527
- HCF of 69, 79, 747, 759
- HCF of 36, 45, 60
- HCF of 120, 150
- HCF of 150, 200, 180
- HCF of 20, 30, 50
- HCF of 21, 35, 49
- HCF of 150, 140, 210
- HCF of 96, 72
- HCF of 26, 32

- HCF of 53, 79, 92, 152
- HCF of 63, 54, 27, 63
- HCF of 210, 128, 362
- HCF of 900, 270
- HCF of 54, 72
- HCF of 480, 192, 295
- HCF of 240, 6552
- HCF of 144, 180, 192
- HCF of 73, 97
- HCF of 670, 480, 372
- HCF of 28, 42, 49
- HCF of 92, 18, 152
- HCF of 204, 1190, 1445
- HCF of 1250, 9375, 15625
- HCF of 22, 45
- HCF of 96, 240, 336
- HCF of 12, 15, 21
- HCF of 75, 69
- HCF of 1517, 902
- HCF of 1651, 2032

- HCF of 100, 190
- HCF of 56, 64, 84, 72
- HCF of 286, 363, 323
- HCF of 108, 24
- HCF of 36, 96
- HCF of 88, 220, 132
- HCF of 35, 42, 30
- HCF of 26, 38, 42
- HCF of 71, 700, 113
- HCF of 25, 41, 609, 957
- HCF of 133, 112
- HCF of 19, 95
- HCF of 60, 36, 530
- HCF of 158, 200
- HCF of 576, 448
- HCF of 32, 624
- HCF of 2, 200, 336
- HCF of 20, 50
- HCF of 51, 85, 153
- HCF of 612, 1314

- HCF of 56, 32, 52, 67
- HCF of 38, 48
- HCF of 40, 80, 120
- HCF of 25, 45
- HCF of 30, 42, 77, 30
- HCF of 32, 58
- HCF of 36, 105, 180
- HCF of 133, 269, 112
- HCF of 403, 301, 889
- HCF of 60, 168, 180
- HCF of 16, 24, 80
- HCF of 75, 51, 65, 631
- HCF of 130, 120, 585
- HCF of 72, 90, 120
- HCF of 961, 155
- HCF of 225, 45
- HCF of 16, 28
- HCF of 27, 63, 18, 754
- HCF of 36, 90, 135
- HCF of 33, 87, 68, 195

**1. What is meant by Euclid’s Division Lemma?**

The definition of Euclid’s Division Lemma is if two positive integers say “a” and “b”, then there exists unique integers state “q” and “r” such that which satisfies the condition a = bq + r where 0 ≤ r ≤ b.

**2. What is Lemma?**

Lemma is a proven statement used for proving another statement.

**3. What represents Q and R in Euclid’s Division Lemma Technique?**

The number ‘q’ is called the quotient and ‘r’ is called the remainder.

**4. What is HCF of two or more numbers?**

The full form of HCF is Highest Common Factor. The HCF of two or more given integers is defined as the greatest number which evenly divides a given set of numbers.

**5. How to Find HCF using Euclid’s Division Lemma?**

You can easily find HCF of a set of integers by Euclid’s division lemma along with a detailed explanation from our page. Enter the inputs and get the HCF of two or more numbers which is solved by using Euclid’s division lemma method with neat & understandable steps.