Highest Common Factor of 377, 523 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 377, 523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 377, 523 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 377, 523 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 377, 523 is 1.

HCF(377, 523) = 1

HCF of 377, 523 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 377, 523 is 1.

Highest Common Factor of 377,523 using Euclid's algorithm

Highest Common Factor of 377,523 is 1

Step 1: Since 523 > 377, we apply the division lemma to 523 and 377, to get

523 = 377 x 1 + 146

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 146 and 377, to get

377 = 146 x 2 + 85

Step 3: We consider the new divisor 146 and the new remainder 85, and apply the division lemma to get

146 = 85 x 1 + 61

We consider the new divisor 85 and the new remainder 61,and apply the division lemma to get

85 = 61 x 1 + 24

We consider the new divisor 61 and the new remainder 24,and apply the division lemma to get

61 = 24 x 2 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 377 and 523 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(61,24) = HCF(85,61) = HCF(146,85) = HCF(377,146) = HCF(523,377) .

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Frequently Asked Questions on HCF of 377, 523 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 377, 523?

Answer: HCF of 377, 523 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 377, 523 using Euclid's Algorithm?

Answer: For arbitrary numbers 377, 523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.