Highest Common Factor of 816, 346, 214 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 816, 346, 214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 816, 346, 214 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 816, 346, 214 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 816, 346, 214 is 2.

HCF(816, 346, 214) = 2

HCF of 816, 346, 214 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 816, 346, 214 is 2.

Highest Common Factor of 816,346,214 using Euclid's algorithm

Highest Common Factor of 816,346,214 is 2

Step 1: Since 816 > 346, we apply the division lemma to 816 and 346, to get

816 = 346 x 2 + 124

Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 124 and 346, to get

346 = 124 x 2 + 98

Step 3: We consider the new divisor 124 and the new remainder 98, and apply the division lemma to get

124 = 98 x 1 + 26

We consider the new divisor 98 and the new remainder 26,and apply the division lemma to get

98 = 26 x 3 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 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 816 and 346 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(98,26) = HCF(124,98) = HCF(346,124) = HCF(816,346) .

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

Step 1: Since 214 > 2, we apply the division lemma to 214 and 2, to get

214 = 2 x 107 + 0

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

Notice that 2 = HCF(214,2) .

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Frequently Asked Questions on HCF of 816, 346, 214 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 816, 346, 214?

Answer: HCF of 816, 346, 214 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 816, 346, 214 using Euclid's Algorithm?

Answer: For arbitrary numbers 816, 346, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.