Highest Common Factor of 211, 972, 582 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 211, 972, 582 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 211, 972, 582 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 211, 972, 582 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 211, 972, 582 is 1.

HCF(211, 972, 582) = 1

HCF of 211, 972, 582 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 211, 972, 582 is 1.

Highest Common Factor of 211,972,582 using Euclid's algorithm

Highest Common Factor of 211,972,582 is 1

Step 1: Since 972 > 211, we apply the division lemma to 972 and 211, to get

972 = 211 x 4 + 128

Step 2: Since the reminder 211 ≠ 0, we apply division lemma to 128 and 211, to get

211 = 128 x 1 + 83

Step 3: We consider the new divisor 128 and the new remainder 83, and apply the division lemma to get

128 = 83 x 1 + 45

We consider the new divisor 83 and the new remainder 45,and apply the division lemma to get

83 = 45 x 1 + 38

We consider the new divisor 45 and the new remainder 38,and apply the division lemma to get

45 = 38 x 1 + 7

We consider the new divisor 38 and the new remainder 7,and apply the division lemma to get

38 = 7 x 5 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 211 and 972 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(38,7) = HCF(45,38) = HCF(83,45) = HCF(128,83) = HCF(211,128) = HCF(972,211) .

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

Step 1: Since 582 > 1, we apply the division lemma to 582 and 1, to get

582 = 1 x 582 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 582 is 1

Notice that 1 = HCF(582,1) .

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Frequently Asked Questions on HCF of 211, 972, 582 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 211, 972, 582?

Answer: HCF of 211, 972, 582 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 211, 972, 582 using Euclid's Algorithm?

Answer: For arbitrary numbers 211, 972, 582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.