Highest Common Factor of 208, 385, 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 208, 385, 676 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 208, 385, 676 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 208, 385, 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 208, 385, 676 is 1.

HCF(208, 385, 676) = 1

HCF of 208, 385, 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 208, 385, 676 is 1.

Highest Common Factor of 208,385,676 using Euclid's algorithm

Highest Common Factor of 208,385,676 is 1

Step 1: Since 385 > 208, we apply the division lemma to 385 and 208, to get

385 = 208 x 1 + 177

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 177 and 208, to get

208 = 177 x 1 + 31

Step 3: We consider the new divisor 177 and the new remainder 31, and apply the division lemma to get

177 = 31 x 5 + 22

We consider the new divisor 31 and the new remainder 22,and apply the division lemma to get

31 = 22 x 1 + 9

We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get

22 = 9 x 2 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 208 and 385 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(31,22) = HCF(177,31) = HCF(208,177) = HCF(385,208) .

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

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

676 = 1 x 676 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 676 is 1

Notice that 1 = HCF(676,1) .

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Frequently Asked Questions on HCF of 208, 385, 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 208, 385, 676?

Answer: HCF of 208, 385, 676 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 208, 385, 676 using Euclid's Algorithm?

Answer: For arbitrary numbers 208, 385, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.