Highest Common Factor of 722, 3397 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 722, 3397 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 722, 3397 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 722, 3397 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 722, 3397 is 1.

HCF(722, 3397) = 1

HCF of 722, 3397 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 722, 3397 is 1.

Highest Common Factor of 722,3397 using Euclid's algorithm

Highest Common Factor of 722,3397 is 1

Step 1: Since 3397 > 722, we apply the division lemma to 3397 and 722, to get

3397 = 722 x 4 + 509

Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 509 and 722, to get

722 = 509 x 1 + 213

Step 3: We consider the new divisor 509 and the new remainder 213, and apply the division lemma to get

509 = 213 x 2 + 83

We consider the new divisor 213 and the new remainder 83,and apply the division lemma to get

213 = 83 x 2 + 47

We consider the new divisor 83 and the new remainder 47,and apply the division lemma to get

83 = 47 x 1 + 36

We consider the new divisor 47 and the new remainder 36,and apply the division lemma to get

47 = 36 x 1 + 11

We consider the new divisor 36 and the new remainder 11,and apply the division lemma to get

36 = 11 x 3 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 722 and 3397 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(36,11) = HCF(47,36) = HCF(83,47) = HCF(213,83) = HCF(509,213) = HCF(722,509) = HCF(3397,722) .

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Frequently Asked Questions on HCF of 722, 3397 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 722, 3397?

Answer: HCF of 722, 3397 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 722, 3397 using Euclid's Algorithm?

Answer: For arbitrary numbers 722, 3397 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.