Highest Common Factor of 408, 722, 797 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 408, 722, 797 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 408, 722, 797 is 1 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 408, 722, 797 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 408, 722, 797 is 1.

HCF(408, 722, 797) = 1

HCF of 408, 722, 797 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 408, 722, 797 is 1.

Highest Common Factor of 408,722,797 using Euclid's algorithm

Highest Common Factor of 408,722,797 is 1

Step 1: Since 722 > 408, we apply the division lemma to 722 and 408, to get

722 = 408 x 1 + 314

Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 314 and 408, to get

408 = 314 x 1 + 94

Step 3: We consider the new divisor 314 and the new remainder 94, and apply the division lemma to get

314 = 94 x 3 + 32

We consider the new divisor 94 and the new remainder 32,and apply the division lemma to get

94 = 32 x 2 + 30

We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get

32 = 30 x 1 + 2

We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get

30 = 2 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 408 and 722 is 2

Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(94,32) = HCF(314,94) = HCF(408,314) = HCF(722,408) .

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

Step 1: Since 797 > 2, we apply the division lemma to 797 and 2, to get

797 = 2 x 398 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 797 is 1

Notice that 1 = HCF(2,1) = HCF(797,2) .

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Frequently Asked Questions on HCF of 408, 722, 797 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 408, 722, 797?

Answer: HCF of 408, 722, 797 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 408, 722, 797 using Euclid's Algorithm?

Answer: For arbitrary numbers 408, 722, 797 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.