Highest Common Factor of 712, 971, 431 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 712, 971, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 971, 431 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 712, 971, 431 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 712, 971, 431 is 1.

HCF(712, 971, 431) = 1

HCF of 712, 971, 431 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 712, 971, 431 is 1.

Highest Common Factor of 712,971,431 using Euclid's algorithm

Highest Common Factor of 712,971,431 is 1

Step 1: Since 971 > 712, we apply the division lemma to 971 and 712, to get

971 = 712 x 1 + 259

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 259 and 712, to get

712 = 259 x 2 + 194

Step 3: We consider the new divisor 259 and the new remainder 194, and apply the division lemma to get

259 = 194 x 1 + 65

We consider the new divisor 194 and the new remainder 65,and apply the division lemma to get

194 = 65 x 2 + 64

We consider the new divisor 65 and the new remainder 64,and apply the division lemma to get

65 = 64 x 1 + 1

We consider the new divisor 64 and the new remainder 1,and apply the division lemma to get

64 = 1 x 64 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 712 and 971 is 1

Notice that 1 = HCF(64,1) = HCF(65,64) = HCF(194,65) = HCF(259,194) = HCF(712,259) = HCF(971,712) .

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

Step 1: Since 431 > 1, we apply the division lemma to 431 and 1, to get

431 = 1 x 431 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 431 is 1

Notice that 1 = HCF(431,1) .

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Frequently Asked Questions on HCF of 712, 971, 431 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 712, 971, 431?

Answer: HCF of 712, 971, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 971, 431 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 971, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.