Highest Common Factor of 591, 908, 520 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 591, 908, 520 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 591, 908, 520 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 591, 908, 520 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 591, 908, 520 is 1.

HCF(591, 908, 520) = 1

HCF of 591, 908, 520 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 591, 908, 520 is 1.

Highest Common Factor of 591,908,520 using Euclid's algorithm

Highest Common Factor of 591,908,520 is 1

Step 1: Since 908 > 591, we apply the division lemma to 908 and 591, to get

908 = 591 x 1 + 317

Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 317 and 591, to get

591 = 317 x 1 + 274

Step 3: We consider the new divisor 317 and the new remainder 274, and apply the division lemma to get

317 = 274 x 1 + 43

We consider the new divisor 274 and the new remainder 43,and apply the division lemma to get

274 = 43 x 6 + 16

We consider the new divisor 43 and the new remainder 16,and apply the division lemma to get

43 = 16 x 2 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

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 591 and 908 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(43,16) = HCF(274,43) = HCF(317,274) = HCF(591,317) = HCF(908,591) .

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

Step 1: Since 520 > 1, we apply the division lemma to 520 and 1, to get

520 = 1 x 520 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 520 is 1

Notice that 1 = HCF(520,1) .

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Frequently Asked Questions on HCF of 591, 908, 520 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 591, 908, 520?

Answer: HCF of 591, 908, 520 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 591, 908, 520 using Euclid's Algorithm?

Answer: For arbitrary numbers 591, 908, 520 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.