HCF of 27, 147, 446 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 27,147,446 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(27,147,446).

Here 147 is greater than 27

Now, consider the largest number as 'a' from the given number ie., 147 and 27 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 147 > 27, we apply the division lemma to 147 and 27, to get

147 = 27 x 5 + 12

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 12 and 27, to get

27 = 12 x 2 + 3

Step 3: We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 147 is 3

Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(147,27) .

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

Here 446 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 446 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 446 > 3, we apply the division lemma to 446 and 3, to get

446 = 3 x 148 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 446 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(446,3) .

Therefore, HCF of 27,147,446 using Euclid's division lemma is 1.