Highest Common Factor of 420, 774, 722 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 420, 774, 722 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 774, 722 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 420, 774, 722 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 420, 774, 722 is 2.

HCF(420, 774, 722) = 2

HCF of 420, 774, 722 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 420, 774, 722 is 2.

Highest Common Factor of 420,774,722 using Euclid's algorithm

Highest Common Factor of 420,774,722 is 2

Step 1: Since 774 > 420, we apply the division lemma to 774 and 420, to get

774 = 420 x 1 + 354

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 354 and 420, to get

420 = 354 x 1 + 66

Step 3: We consider the new divisor 354 and the new remainder 66, and apply the division lemma to get

354 = 66 x 5 + 24

We consider the new divisor 66 and the new remainder 24,and apply the division lemma to get

66 = 24 x 2 + 18

We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get

24 = 18 x 1 + 6

We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 420 and 774 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(66,24) = HCF(354,66) = HCF(420,354) = HCF(774,420) .

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

Step 1: Since 722 > 6, we apply the division lemma to 722 and 6, to get

722 = 6 x 120 + 2

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 722 is 2

Notice that 2 = HCF(6,2) = HCF(722,6) .

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Frequently Asked Questions on HCF of 420, 774, 722 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 420, 774, 722?

Answer: HCF of 420, 774, 722 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 774, 722 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 774, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.