Highest Common Factor of 588, 377 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 588, 377 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 588, 377 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 588, 377 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 588, 377 is 1.

HCF(588, 377) = 1

HCF of 588, 377 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 588, 377 is 1.

Highest Common Factor of 588,377 using Euclid's algorithm

Highest Common Factor of 588,377 is 1

Step 1: Since 588 > 377, we apply the division lemma to 588 and 377, to get

588 = 377 x 1 + 211

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 211 and 377, to get

377 = 211 x 1 + 166

Step 3: We consider the new divisor 211 and the new remainder 166, and apply the division lemma to get

211 = 166 x 1 + 45

We consider the new divisor 166 and the new remainder 45,and apply the division lemma to get

166 = 45 x 3 + 31

We consider the new divisor 45 and the new remainder 31,and apply the division lemma to get

45 = 31 x 1 + 14

We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get

31 = 14 x 2 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 588 and 377 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(45,31) = HCF(166,45) = HCF(211,166) = HCF(377,211) = HCF(588,377) .

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Frequently Asked Questions on HCF of 588, 377 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 588, 377?

Answer: HCF of 588, 377 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 588, 377 using Euclid's Algorithm?

Answer: For arbitrary numbers 588, 377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.