HCF of 105, 147, 189 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 105,147,189 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(105,147,189).

Here 147 is greater than 105

Now, consider the largest number as 'a' from the given number ie., 147 and 105 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 147 > 105, we apply the division lemma to 147 and 105, to get

147 = 105 x 1 + 42

Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 42 and 105, to get

105 = 42 x 2 + 21

Step 3: We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get

42 = 21 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 105 and 147 is 21

Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(147,105) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 189 is greater than 21

Now, consider the largest number as 'a' from the given number ie., 189 and 21 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 189 > 21, we apply the division lemma to 189 and 21, to get

189 = 21 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 21 and 189 is 21

Notice that 21 = HCF(189,21) .

Therefore, HCF of 105,147,189 using Euclid's division lemma is 21.