Highest Common Factor of 208, 974, 697 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, 974, 697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 208, 974, 697 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, 974, 697 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, 974, 697 is 1.

HCF(208, 974, 697) = 1

HCF of 208, 974, 697 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, 974, 697 is 1.

Highest Common Factor of 208,974,697 using Euclid's algorithm

Highest Common Factor of 208,974,697 is 1

Step 1: Since 974 > 208, we apply the division lemma to 974 and 208, to get

974 = 208 x 4 + 142

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 142 and 208, to get

208 = 142 x 1 + 66

Step 3: We consider the new divisor 142 and the new remainder 66, and apply the division lemma to get

142 = 66 x 2 + 10

We consider the new divisor 66 and the new remainder 10,and apply the division lemma to get

66 = 10 x 6 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 208 and 974 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(142,66) = HCF(208,142) = HCF(974,208) .

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

Step 1: Since 697 > 2, we apply the division lemma to 697 and 2, to get

697 = 2 x 348 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 697 is 1

Notice that 1 = HCF(2,1) = HCF(697,2) .

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Frequently Asked Questions on HCF of 208, 974, 697 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, 974, 697?

Answer: HCF of 208, 974, 697 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 208, 974, 697 using Euclid's Algorithm?

Answer: For arbitrary numbers 208, 974, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.