Highest Common Factor of 520, 668, 165 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, 668, 165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 520, 668, 165 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, 668, 165 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, 668, 165 is 1.

HCF(520, 668, 165) = 1

HCF of 520, 668, 165 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 520, 668, 165 is 1.

Highest Common Factor of 520,668,165 using Euclid's algorithm

Highest Common Factor of 520,668,165 is 1

Step 1: Since 668 > 520, we apply the division lemma to 668 and 520, to get

668 = 520 x 1 + 148

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 148 and 520, to get

520 = 148 x 3 + 76

Step 3: We consider the new divisor 148 and the new remainder 76, and apply the division lemma to get

148 = 76 x 1 + 72

We consider the new divisor 76 and the new remainder 72,and apply the division lemma to get

76 = 72 x 1 + 4

We consider the new divisor 72 and the new remainder 4,and apply the division lemma to get

72 = 4 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 520 and 668 is 4

Notice that 4 = HCF(72,4) = HCF(76,72) = HCF(148,76) = HCF(520,148) = HCF(668,520) .

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

Step 1: Since 165 > 4, we apply the division lemma to 165 and 4, to get

165 = 4 x 41 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 165 is 1

Notice that 1 = HCF(4,1) = HCF(165,4) .

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Frequently Asked Questions on HCF of 520, 668, 165 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, 668, 165?

Answer: HCF of 520, 668, 165 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 520, 668, 165 using Euclid's Algorithm?

Answer: For arbitrary numbers 520, 668, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.