HCF of 69, 78 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 69, 78 is 3.

HCF(69, 78) = 3

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

Below detailed show work will make you learn how to find HCF of 69,78 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(69,78).

Here 78 is greater than 69

Now, consider the largest number as 'a' from the given number ie., 78 and 69 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

**Step 1:** Since 78 > 69, we apply the division lemma to 78 and 69, to get

78 = 69 x 1 + 9

**Step 2:** Since the reminder 69 ≠ 0, we apply division lemma to 9 and 69, to get

69 = 9 x 7 + 6

**Step 3:** We consider the new divisor 9 and the new remainder 6, and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 69 and 78 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(69,9) = HCF(78,69) .

Therefore, HCF of 69,78 using Euclid's division lemma is 3.

Here are some samples of HCF using Euclid's Algorithm calculations.

**1. What is the HCF(69, 78)?**

The Highest common factor of 69, 78 is 3 the largest common factor that exactly divides two or more numbers with remainder 0.

**2. How do you find HCF of 69, 78 using the Euclidean division algorithm?**

According to the Euclidean division algorithm, if we have two integers say a, b ie., 69, 78 the largest number should satisfy Euclid's statement a = bq + r where 0 ≤ r < b and get the highest common factor of 69, 78 as 3.

**3. Where can I get a detailed solution for finding the HCF(69, 78) by Euclid's division lemma method?**

You can get a detailed solution for finding the HCF(69, 78) by Euclid's division lemma method on our page.