Highest Common Factor of 520, 722, 597 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 520, 722, 597 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 520, 722, 597 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 520, 722, 597 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 520, 722, 597 is 1.

HCF(520, 722, 597) = 1

HCF of 520, 722, 597 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 520, 722, 597 is 1.

Highest Common Factor of 520,722,597 using Euclid's algorithm

Highest Common Factor of 520,722,597 is 1

Step 1: Since 722 > 520, we apply the division lemma to 722 and 520, to get

722 = 520 x 1 + 202

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 202 and 520, to get

520 = 202 x 2 + 116

Step 3: We consider the new divisor 202 and the new remainder 116, and apply the division lemma to get

202 = 116 x 1 + 86

We consider the new divisor 116 and the new remainder 86,and apply the division lemma to get

116 = 86 x 1 + 30

We consider the new divisor 86 and the new remainder 30,and apply the division lemma to get

86 = 30 x 2 + 26

We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get

30 = 26 x 1 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 520 and 722 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(86,30) = HCF(116,86) = HCF(202,116) = HCF(520,202) = HCF(722,520) .

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

Step 1: Since 597 > 2, we apply the division lemma to 597 and 2, to get

597 = 2 x 298 + 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 597 is 1

Notice that 1 = HCF(2,1) = HCF(597,2) .

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Frequently Asked Questions on HCF of 520, 722, 597 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 520, 722, 597?

Answer: HCF of 520, 722, 597 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 520, 722, 597 using Euclid's Algorithm?

Answer: For arbitrary numbers 520, 722, 597 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.