Highest Common Factor of 214, 344, 74 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 214, 344, 74 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 214, 344, 74 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 214, 344, 74 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 214, 344, 74 is 2.

HCF(214, 344, 74) = 2

HCF of 214, 344, 74 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 214, 344, 74 is 2.

Highest Common Factor of 214,344,74 using Euclid's algorithm

Highest Common Factor of 214,344,74 is 2

Step 1: Since 344 > 214, we apply the division lemma to 344 and 214, to get

344 = 214 x 1 + 130

Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 130 and 214, to get

214 = 130 x 1 + 84

Step 3: We consider the new divisor 130 and the new remainder 84, and apply the division lemma to get

130 = 84 x 1 + 46

We consider the new divisor 84 and the new remainder 46,and apply the division lemma to get

84 = 46 x 1 + 38

We consider the new divisor 46 and the new remainder 38,and apply the division lemma to get

46 = 38 x 1 + 8

We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get

38 = 8 x 4 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 214 and 344 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(46,38) = HCF(84,46) = HCF(130,84) = HCF(214,130) = HCF(344,214) .

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

Step 1: Since 74 > 2, we apply the division lemma to 74 and 2, to get

74 = 2 x 37 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 74 is 2

Notice that 2 = HCF(74,2) .

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Frequently Asked Questions on HCF of 214, 344, 74 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 214, 344, 74?

Answer: HCF of 214, 344, 74 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 214, 344, 74 using Euclid's Algorithm?

Answer: For arbitrary numbers 214, 344, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.