Highest Common Factor of 520, 764, 70 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, 764, 70 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 520, 764, 70 is 2 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, 764, 70 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, 764, 70 is 2.

HCF(520, 764, 70) = 2

HCF of 520, 764, 70 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, 764, 70 is 2.

Highest Common Factor of 520,764,70 using Euclid's algorithm

Highest Common Factor of 520,764,70 is 2

Step 1: Since 764 > 520, we apply the division lemma to 764 and 520, to get

764 = 520 x 1 + 244

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 244 and 520, to get

520 = 244 x 2 + 32

Step 3: We consider the new divisor 244 and the new remainder 32, and apply the division lemma to get

244 = 32 x 7 + 20

We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get

32 = 20 x 1 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 520 and 764 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(244,32) = HCF(520,244) = HCF(764,520) .

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

Step 1: Since 70 > 4, we apply the division lemma to 70 and 4, to get

70 = 4 x 17 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 70 is 2

Notice that 2 = HCF(4,2) = HCF(70,4) .

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Frequently Asked Questions on HCF of 520, 764, 70 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, 764, 70?

Answer: HCF of 520, 764, 70 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 520, 764, 70 using Euclid's Algorithm?

Answer: For arbitrary numbers 520, 764, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.