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HCF of 120, 68 using Euclid's algorithm

HCF of 120, 68 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., 4 the largest factor that exactly divides the numbers with r=0.

Highest common factor (HCF) of 120, 68 is 4.

HCF(120, 68) = 4

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

HCF of

Determining HCF of Numbers 120,68 by Euclid's Division Lemma

Below detailed show work will make you learn how to find HCF of 120,68 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(120,68).

Here 120 is greater than 68

Now, consider the largest number as 'a' from the given number ie., 120 and 68 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 120 > 68, we apply the division lemma to 120 and 68, to get

120 = 68 x 1 + 52

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 52 and 68, to get

68 = 52 x 1 + 16

Step 3: We consider the new divisor 52 and the new remainder 16, and apply the division lemma to get

52 = 16 x 3 + 4

We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 120 and 68 is 4

Notice that 4 = HCF(16,4) = HCF(52,16) = HCF(68,52) = HCF(120,68) .

Therefore, HCF of 120,68 using Euclid's division lemma is 4.

HCF using Euclid's Algorithm Calculation Examples

FAQs on HCF of 120, 68 using Euclid's Division Lemma Algorithm

1. What is the HCF(120, 68)?

The Highest common factor of 120, 68 is 4 the largest common factor that exactly divides two or more numbers with remainder 0.


2. How do you find HCF of 120, 68 using the Euclidean division algorithm?

According to the Euclidean division algorithm, if we have two integers say a, b ie., 120, 68 the largest number should satisfy Euclid's statement a = bq + r where 0 ≤ r < b and get the highest common factor of 120, 68 as 4.


3. Where can I get a detailed solution for finding the HCF(120, 68) by Euclid's division lemma method?

You can get a detailed solution for finding the HCF(120, 68) by Euclid's division lemma method on our page.