Highest Common Factor of 340, 466, 676 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 340, 466, 676 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 340, 466, 676 is 2 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 340, 466, 676 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 340, 466, 676 is 2.

HCF(340, 466, 676) = 2

HCF of 340, 466, 676 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 340, 466, 676 is 2.

Highest Common Factor of 340,466,676 using Euclid's algorithm

Highest Common Factor of 340,466,676 is 2

Step 1: Since 466 > 340, we apply the division lemma to 466 and 340, to get

466 = 340 x 1 + 126

Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 126 and 340, to get

340 = 126 x 2 + 88

Step 3: We consider the new divisor 126 and the new remainder 88, and apply the division lemma to get

126 = 88 x 1 + 38

We consider the new divisor 88 and the new remainder 38,and apply the division lemma to get

88 = 38 x 2 + 12

We consider the new divisor 38 and the new remainder 12,and apply the division lemma to get

38 = 12 x 3 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 340 and 466 is 2

Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(88,38) = HCF(126,88) = HCF(340,126) = HCF(466,340) .

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

Step 1: Since 676 > 2, we apply the division lemma to 676 and 2, to get

676 = 2 x 338 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 676 is 2

Notice that 2 = HCF(676,2) .

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Frequently Asked Questions on HCF of 340, 466, 676 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 340, 466, 676?

Answer: HCF of 340, 466, 676 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 340, 466, 676 using Euclid's Algorithm?

Answer: For arbitrary numbers 340, 466, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.