HCF Using Euclid's division lemma Calculator is a free online tool that easily calculates the highest common factor of two or more numbers using Euclid's division lemma method. All you have to provide is given two or three numbers in the input box and hit on the calculator button to avail the HCF of given numbers in less time.

**Ex:** 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345

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

**HCF Using Euclid's division lemma Calculator:** Guys who are really excited to learn how to find the HCF of two or more numbers using Euclid's division lemma method can stick to this page. Here, we have discussed the step by step procedure on finding the Highest common factor of given numbers using the Euclid's Algorithm. So, Look no further and just dig deep into this article to know how Euclid's division lemma works while finding the HCF.

Before going to start the detailed process of finding HCF using Euclid's division lemma method once have a look at the Euclidean division algorithm. The foundation of the Euclidean division algorithm is known as Euclid’s division lemma.

As per the Euclid’s Division Lemma if you take two positive integers (just say a and b), then there prevail two unique integers q and r that fulfills the condition **a = bq + r** where 0 ≤ r < b.

Mostly, this Euclid’s Division Lemma is used to find out the Highest Common Factor of Two or more given numbers. Here you will get to see the detailed steps on how to find the HCF using Euclid's division lemma algorithm. Okay, let's begin the process of calculating the highest common factors of two or more given numbers easily.

- Mostly, this Euclid’s Division Lemma is used to find out the Highest Common Factor of Two or more given numbers. Here you will get to see the detailed steps on how to find the HCF using Euclid's division lemma algorithm. Okay, let's begin the process of calculating the highest common factors of two or more given numbers easily.
- After applying the algorithm to the given numbers, you will find the quotient and remainder for the largest number.
- If the remainder is zero, then b is the HCF of the given numbers.
- In case the remainder is not equal to zero, then repeat Euclid's division lemma to b and r.
- Keep on repeating the same process until you get r=0. Finally, the HCF of given numbers say a and b is the division with remainder 0.

**Example:**

Find the HCF of 90, 135 using Euclid's Division Lemma method?

**Solution:**

Given two numbers are 90, 135

Here 135 is greater than 90

Now, consider the largest number as 'a' from the given number ie., 135 and meet the Euclid's statement

a = bq + r where 0 ≤ r < b

135 = 90 x 1 + 45

As remainder≠0, we have to apply Euclid's division lemma for 45 and 90.

90 = 45 x 2 + 0, r=0

The remainder becomes zero, so the divisor is the actual result for HCF of the given number.

Therefore, HCF(90, 135) is **45**.

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- HCF of 6, 10, 11, 14
- HCF of 24, 32, 52, 72
- HCF of 28, 63, 70, 72
- HCF of 30, 48, 60, 66
- HCF of 18, 24, 63, 84
- HCF of 16, 36, 80, 100
- HCF of 240, 260, 370
- HCF of 150, 250, 375
- HCF of 15, 45, 90
- HCF of 21, 24, 27
- HCF of 18, 24, 60
- HCF of 30, 264, 495
- HCF of 18, 27, 147
- HCF of 63, 81, 108, 120
- HCF of 21, 35, 49
- HCF of 20, 50, 100
- HCF of 15, 45, 60
- HCF of 12, 15, 18
- HCF of 25, 35, 45
- HCF of 108, 120, 144
- HCF of 15, 25, 30
- HCF of 26, 39, 52
- HCF of 36, 54, 135
- HCF of 64, 72, 96
- HCF of 36, 42, 98
- HCF of 108, 180, 288

- HCF of 78, 156, 169
- HCF of 12, 20, 28
- HCF of 54, 63, 180
- HCF of 21, 40, 84, 98
- HCF of 36, 48, 60, 108
- HCF of 100, 105, 125, 128
- HCF of 27, 45, 63
- HCF of 25, 75, 100
- HCF of 27, 147, 446
- HCF of 144, 185, 259
- HCF of 50, 220, 242
- HCF of 12, 48, 60
- HCF of 20, 30, 50
- HCF of 18, 42, 60
- HCF of 105, 147, 189
- HCF of 42, 126, 210
- HCF of 28, 42, 49
- HCF of 36, 90, 135
- HCF of 52, 65, 91
- HCF of 56, 84, 112
- HCF of 21, 30, 44
- HCF of 7, 150, 392
- HCF of 90, 135, 180
- HCF of 45, 60, 120
- HCF of 105, 128, 180

- HCF of 9, 156, 169
- HCF of 12, 28, 56
- HCF of 36, 54, 126
- HCF of 14, 21, 28
- HCF of 20, 30, 70
- HCF of 135, 180, 225
- HCF of 125, 180, 300
- HCF of 54, 90, 108
- HCF of 51, 85, 153
- HCF of 14, 49, 63
- HCF of 9, 12, 21
- HCF of 45, 60, 150
- HCF of 16, 32, 40
- HCF of 36, 60, 135
- HCF of 135, 225, 315
- HCF of 18, 30, 54
- HCF of 84, 210, 336
- HCF of 24, 28, 32
- HCF of 60, 84, 140
- HCF of 76, 80, 88, 125
- HCF of 16, 20, 24, 32
- HCF of 27, 45, 108, 126
- HCF of 15, 35, 42, 68
- HCF of 40, 48, 60, 95
- HCF of 56, 60, 63, 121

**1. Define Euclid's Division Lemma?**

Euclid's Division Lemma states that, if two positive integers 'a' and 'b', then there exist unique integers 'q' and 'r' that satisfies the condition **a = bq + r** where 0 ≤ r ≤ b.

**2. What is meant by HCF of given numbers?**

Highest Common Factor (HCF) of given numbers is the largest or greatest factor common to any two or more given numbers. Also known as GCF or GCD (Greatest Common Divisor).

**3. How to find HCF of two or more numbers using the Euclidean division algorithm on a calculator?**

You can easily find the highest common factor of two or more numbers by taking help from HCF Using Euclid's division lemma Calculator. Just enter the input numbers in the input box and hit on the calculate button.

**4. Can I easily calculate the HCF of two or more numbers Using Euclid's division lemma?**

Yes, you can easily calculate the HCF of two or more numbers Using Euclid's division lemma by following the steps provided above and use the free online calculator available on the screen.