Highest Common Factor of 712, 197, 458 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, 197, 458 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 197, 458 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, 197, 458 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, 197, 458 is 1.

HCF(712, 197, 458) = 1

HCF of 712, 197, 458 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, 197, 458 is 1.

Highest Common Factor of 712,197,458 using Euclid's algorithm

Highest Common Factor of 712,197,458 is 1

Step 1: Since 712 > 197, we apply the division lemma to 712 and 197, to get

712 = 197 x 3 + 121

Step 2: Since the reminder 197 ≠ 0, we apply division lemma to 121 and 197, to get

197 = 121 x 1 + 76

Step 3: We consider the new divisor 121 and the new remainder 76, and apply the division lemma to get

121 = 76 x 1 + 45

We consider the new divisor 76 and the new remainder 45,and apply the division lemma to get

76 = 45 x 1 + 31

We consider the new divisor 45 and the new remainder 31,and apply the division lemma to get

45 = 31 x 1 + 14

We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get

31 = 14 x 2 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 712 and 197 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(45,31) = HCF(76,45) = HCF(121,76) = HCF(197,121) = HCF(712,197) .

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

Step 1: Since 458 > 1, we apply the division lemma to 458 and 1, to get

458 = 1 x 458 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 458 is 1

Notice that 1 = HCF(458,1) .

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Frequently Asked Questions on HCF of 712, 197, 458 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, 197, 458?

Answer: HCF of 712, 197, 458 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 197, 458 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 197, 458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.