Highest Common Factor of 774, 212, 50 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 774, 212, 50 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 774, 212, 50 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 774, 212, 50 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 774, 212, 50 is 2.

HCF(774, 212, 50) = 2

HCF of 774, 212, 50 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 774, 212, 50 is 2.

Highest Common Factor of 774,212,50 using Euclid's algorithm

Highest Common Factor of 774,212,50 is 2

Step 1: Since 774 > 212, we apply the division lemma to 774 and 212, to get

774 = 212 x 3 + 138

Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 138 and 212, to get

212 = 138 x 1 + 74

Step 3: We consider the new divisor 138 and the new remainder 74, and apply the division lemma to get

138 = 74 x 1 + 64

We consider the new divisor 74 and the new remainder 64,and apply the division lemma to get

74 = 64 x 1 + 10

We consider the new divisor 64 and the new remainder 10,and apply the division lemma to get

64 = 10 x 6 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 774 and 212 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(64,10) = HCF(74,64) = HCF(138,74) = HCF(212,138) = HCF(774,212) .

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

Step 1: Since 50 > 2, we apply the division lemma to 50 and 2, to get

50 = 2 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 50 is 2

Notice that 2 = HCF(50,2) .

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Frequently Asked Questions on HCF of 774, 212, 50 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 774, 212, 50?

Answer: HCF of 774, 212, 50 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 774, 212, 50 using Euclid's Algorithm?

Answer: For arbitrary numbers 774, 212, 50 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.