Highest Common Factor of 691, 996, 522 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 691, 996, 522 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 996, 522 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 691, 996, 522 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 691, 996, 522 is 1.

HCF(691, 996, 522) = 1

HCF of 691, 996, 522 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 691, 996, 522 is 1.

Highest Common Factor of 691,996,522 using Euclid's algorithm

Highest Common Factor of 691,996,522 is 1

Step 1: Since 996 > 691, we apply the division lemma to 996 and 691, to get

996 = 691 x 1 + 305

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 305 and 691, to get

691 = 305 x 2 + 81

Step 3: We consider the new divisor 305 and the new remainder 81, and apply the division lemma to get

305 = 81 x 3 + 62

We consider the new divisor 81 and the new remainder 62,and apply the division lemma to get

81 = 62 x 1 + 19

We consider the new divisor 62 and the new remainder 19,and apply the division lemma to get

62 = 19 x 3 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 691 and 996 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(62,19) = HCF(81,62) = HCF(305,81) = HCF(691,305) = HCF(996,691) .

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

Step 1: Since 522 > 1, we apply the division lemma to 522 and 1, to get

522 = 1 x 522 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 522 is 1

Notice that 1 = HCF(522,1) .

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Frequently Asked Questions on HCF of 691, 996, 522 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 691, 996, 522?

Answer: HCF of 691, 996, 522 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 996, 522 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 996, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.