HCF of 45, 75, 90, 123 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 45,75,90,123 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(45,75,90,123).

Here 75 is greater than 45

Now, consider the largest number as 'a' from the given number ie., 75 and 45 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 75 > 45, we apply the division lemma to 75 and 45, to get

75 = 45 x 1 + 30

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 30 and 45, to get

45 = 30 x 1 + 15

Step 3: We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 45 and 75 is 15

Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(75,45) .

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

Here 90 is greater than 15

Now, consider the largest number as 'a' from the given number ie., 90 and 15 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 90 > 15, we apply the division lemma to 90 and 15, to get

90 = 15 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 15 and 90 is 15

Notice that 15 = HCF(90,15) .

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

Here 123 is greater than 15

Now, consider the largest number as 'a' from the given number ie., 123 and 15 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 123 > 15, we apply the division lemma to 123 and 15, to get

123 = 15 x 8 + 3

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 3 and 15, to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 123 is 3

Notice that 3 = HCF(15,3) = HCF(123,15) .

Therefore, HCF of 45,75,90,123 using Euclid's division lemma is 3.