Highest Common Factor of 320, 521, 211 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 320, 521, 211 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 320, 521, 211 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 320, 521, 211 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 320, 521, 211 is 1.

HCF(320, 521, 211) = 1

HCF of 320, 521, 211 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 320, 521, 211 is 1.

Highest Common Factor of 320,521,211 using Euclid's algorithm

Highest Common Factor of 320,521,211 is 1

Step 1: Since 521 > 320, we apply the division lemma to 521 and 320, to get

521 = 320 x 1 + 201

Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 201 and 320, to get

320 = 201 x 1 + 119

Step 3: We consider the new divisor 201 and the new remainder 119, and apply the division lemma to get

201 = 119 x 1 + 82

We consider the new divisor 119 and the new remainder 82,and apply the division lemma to get

119 = 82 x 1 + 37

We consider the new divisor 82 and the new remainder 37,and apply the division lemma to get

82 = 37 x 2 + 8

We consider the new divisor 37 and the new remainder 8,and apply the division lemma to get

37 = 8 x 4 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 320 and 521 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(37,8) = HCF(82,37) = HCF(119,82) = HCF(201,119) = HCF(320,201) = HCF(521,320) .

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

Step 1: Since 211 > 1, we apply the division lemma to 211 and 1, to get

211 = 1 x 211 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 211 is 1

Notice that 1 = HCF(211,1) .

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Frequently Asked Questions on HCF of 320, 521, 211 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 320, 521, 211?

Answer: HCF of 320, 521, 211 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 320, 521, 211 using Euclid's Algorithm?

Answer: For arbitrary numbers 320, 521, 211 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.