HCF of 144, 185, 259 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 144,185,259 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(144,185,259).

Here 185 is greater than 144

Now, consider the largest number as 'a' from the given number ie., 185 and 144 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 185 > 144, we apply the division lemma to 185 and 144, to get

185 = 144 x 1 + 41

Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 41 and 144, to get

144 = 41 x 3 + 21

Step 3: We consider the new divisor 41 and the new remainder 21, and apply the division lemma to get

41 = 21 x 1 + 20

We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get

21 = 20 x 1 + 1

We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 144 and 185 is 1

Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(41,21) = HCF(144,41) = HCF(185,144) .

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

Here 259 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 259 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 259 > 1, we apply the division lemma to 259 and 1, to get

259 = 1 x 259 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 259 is 1

Notice that 1 = HCF(259,1) .

Therefore, HCF of 144,185,259 using Euclid's division lemma is 1.