Highest Common Factor of 520, 707, 210, 721 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, 707, 210, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 520, 707, 210, 721 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, 707, 210, 721 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, 707, 210, 721 is 1.

HCF(520, 707, 210, 721) = 1

HCF of 520, 707, 210, 721 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, 707, 210, 721 is 1.

Highest Common Factor of 520,707,210,721 using Euclid's algorithm

Highest Common Factor of 520,707,210,721 is 1

Step 1: Since 707 > 520, we apply the division lemma to 707 and 520, to get

707 = 520 x 1 + 187

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 187 and 520, to get

520 = 187 x 2 + 146

Step 3: We consider the new divisor 187 and the new remainder 146, and apply the division lemma to get

187 = 146 x 1 + 41

We consider the new divisor 146 and the new remainder 41,and apply the division lemma to get

146 = 41 x 3 + 23

We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get

41 = 23 x 1 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 520 and 707 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(146,41) = HCF(187,146) = HCF(520,187) = HCF(707,520) .

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

Step 1: Since 210 > 1, we apply the division lemma to 210 and 1, to get

210 = 1 x 210 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 210 is 1

Notice that 1 = HCF(210,1) .

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

Step 1: Since 721 > 1, we apply the division lemma to 721 and 1, to get

721 = 1 x 721 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 721 is 1

Notice that 1 = HCF(721,1) .

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Frequently Asked Questions on HCF of 520, 707, 210, 721 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, 707, 210, 721?

Answer: HCF of 520, 707, 210, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 520, 707, 210, 721 using Euclid's Algorithm?

Answer: For arbitrary numbers 520, 707, 210, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.