Highest Common Factor of 339, 208, 414 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 339, 208, 414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 339, 208, 414 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 339, 208, 414 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 339, 208, 414 is 1.

HCF(339, 208, 414) = 1

HCF of 339, 208, 414 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 339, 208, 414 is 1.

Highest Common Factor of 339,208,414 using Euclid's algorithm

Highest Common Factor of 339,208,414 is 1

Step 1: Since 339 > 208, we apply the division lemma to 339 and 208, to get

339 = 208 x 1 + 131

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 131 and 208, to get

208 = 131 x 1 + 77

Step 3: We consider the new divisor 131 and the new remainder 77, and apply the division lemma to get

131 = 77 x 1 + 54

We consider the new divisor 77 and the new remainder 54,and apply the division lemma to get

77 = 54 x 1 + 23

We consider the new divisor 54 and the new remainder 23,and apply the division lemma to get

54 = 23 x 2 + 8

We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get

23 = 8 x 2 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 339 and 208 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(54,23) = HCF(77,54) = HCF(131,77) = HCF(208,131) = HCF(339,208) .

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

Step 1: Since 414 > 1, we apply the division lemma to 414 and 1, to get

414 = 1 x 414 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 414 is 1

Notice that 1 = HCF(414,1) .

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Frequently Asked Questions on HCF of 339, 208, 414 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 339, 208, 414?

Answer: HCF of 339, 208, 414 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 339, 208, 414 using Euclid's Algorithm?

Answer: For arbitrary numbers 339, 208, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.