Highest Common Factor of 662, 522, 681 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 662, 522, 681 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 662, 522, 681 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 662, 522, 681 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 662, 522, 681 is 1.

HCF(662, 522, 681) = 1

HCF of 662, 522, 681 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 662, 522, 681 is 1.

Highest Common Factor of 662,522,681 using Euclid's algorithm

Highest Common Factor of 662,522,681 is 1

Step 1: Since 662 > 522, we apply the division lemma to 662 and 522, to get

662 = 522 x 1 + 140

Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 140 and 522, to get

522 = 140 x 3 + 102

Step 3: We consider the new divisor 140 and the new remainder 102, and apply the division lemma to get

140 = 102 x 1 + 38

We consider the new divisor 102 and the new remainder 38,and apply the division lemma to get

102 = 38 x 2 + 26

We consider the new divisor 38 and the new remainder 26,and apply the division lemma to get

38 = 26 x 1 + 12

We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get

26 = 12 x 2 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 662 and 522 is 2

Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(38,26) = HCF(102,38) = HCF(140,102) = HCF(522,140) = HCF(662,522) .

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

Step 1: Since 681 > 2, we apply the division lemma to 681 and 2, to get

681 = 2 x 340 + 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 681 is 1

Notice that 1 = HCF(2,1) = HCF(681,2) .

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Frequently Asked Questions on HCF of 662, 522, 681 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 662, 522, 681?

Answer: HCF of 662, 522, 681 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 662, 522, 681 using Euclid's Algorithm?

Answer: For arbitrary numbers 662, 522, 681 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.