HCF of 125, 180, 300 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 125,180,300 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(125,180,300).

Here 180 is greater than 125

Now, consider the largest number as 'a' from the given number ie., 180 and 125 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 180 > 125, we apply the division lemma to 180 and 125, to get

180 = 125 x 1 + 55

Step 2: Since the reminder 125 ≠ 0, we apply division lemma to 55 and 125, to get

125 = 55 x 2 + 15

Step 3: We consider the new divisor 55 and the new remainder 15, and apply the division lemma to get

55 = 15 x 3 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 125 and 180 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) = HCF(125,55) = HCF(180,125) .

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

Here 300 is greater than 5

Now, consider the largest number as 'a' from the given number ie., 300 and 5 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 300 > 5, we apply the division lemma to 300 and 5, to get

300 = 5 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 300 is 5

Notice that 5 = HCF(300,5) .

Therefore, HCF of 125,180,300 using Euclid's division lemma is 5.