Highest Common Factor of 522, 660, 635 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 522, 660, 635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 522, 660, 635 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 522, 660, 635 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 522, 660, 635 is 1.

HCF(522, 660, 635) = 1

HCF of 522, 660, 635 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 522, 660, 635 is 1.

Highest Common Factor of 522,660,635 using Euclid's algorithm

Highest Common Factor of 522,660,635 is 1

Step 1: Since 660 > 522, we apply the division lemma to 660 and 522, to get

660 = 522 x 1 + 138

Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 138 and 522, to get

522 = 138 x 3 + 108

Step 3: We consider the new divisor 138 and the new remainder 108, and apply the division lemma to get

138 = 108 x 1 + 30

We consider the new divisor 108 and the new remainder 30,and apply the division lemma to get

108 = 30 x 3 + 18

We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get

30 = 18 x 1 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 522 and 660 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(108,30) = HCF(138,108) = HCF(522,138) = HCF(660,522) .

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

Step 1: Since 635 > 6, we apply the division lemma to 635 and 6, to get

635 = 6 x 105 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 635 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(635,6) .

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Frequently Asked Questions on HCF of 522, 660, 635 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 522, 660, 635?

Answer: HCF of 522, 660, 635 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 522, 660, 635 using Euclid's Algorithm?

Answer: For arbitrary numbers 522, 660, 635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.