# HCF of 51, 21 using Euclid's algorithm

HCF of 51, 21 by Euclid's Divison lemma method can be determined easily by using our free online HCF using Euclid's Divison Lemma Calculator and get the result in a fraction of seconds ie., 3 the largest factor that exactly divides the numbers with r=0.

Highest common factor (HCF) of 51, 21 is 3.

HCF(51, 21) = 3

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

HCF of

## Determining HCF of Numbers 51,21 by Euclid's Division Lemma

Below detailed show work will make you learn how to find HCF of 51,21 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(51,21).

Here 51 is greater than 21

Now, consider the largest number as 'a' from the given number ie., 51 and 21 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 51 > 21, we apply the division lemma to 51 and 21, to get

51 = 21 x 2 + 9

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 9 and 21, to get

21 = 9 x 2 + 3

Step 3: We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 51 and 21 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) .

Therefore, HCF of 51,21 using Euclid's division lemma is 3.

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### FAQs on HCF of 51, 21 using Euclid's Division Lemma Algorithm

1. What is the HCF(51, 21)?

The Highest common factor of 51, 21 is 3 the largest common factor that exactly divides two or more numbers with remainder 0.

2. How do you find HCF of 51, 21 using the Euclidean division algorithm?

According to the Euclidean division algorithm, if we have two integers say a, b ie., 51, 21 the largest number should satisfy Euclid's statement a = bq + r where 0 ≤ r < b and get the highest common factor of 51, 21 as 3.

3. Where can I get a detailed solution for finding the HCF(51, 21) by Euclid's division lemma method?

You can get a detailed solution for finding the HCF(51, 21) by Euclid's division lemma method on our page.