HCF of 625, 369, 144 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 625,369,144 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(625,369,144).

Here 625 is greater than 369

Now, consider the largest number as 'a' from the given number ie., 625 and 369 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 625 > 369, we apply the division lemma to 625 and 369, to get

625 = 369 x 1 + 256

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 256 and 369, to get

369 = 256 x 1 + 113

Step 3: We consider the new divisor 256 and the new remainder 113, and apply the division lemma to get

256 = 113 x 2 + 30

We consider the new divisor 113 and the new remainder 30,and apply the division lemma to get

113 = 30 x 3 + 23

We consider the new divisor 30 and the new remainder 23,and apply the division lemma to get

30 = 23 x 1 + 7

We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get

23 = 7 x 3 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

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 625 and 369 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(30,23) = HCF(113,30) = HCF(256,113) = HCF(369,256) = HCF(625,369) .

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

Here 144 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 144 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

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

144 = 1 x 144 + 0

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

Notice that 1 = HCF(144,1) .

Therefore, HCF of 625,369,144 using Euclid's division lemma is 1.