Highest Common Factor of 257, 691, 862 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 257, 691, 862 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 257, 691, 862 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 257, 691, 862 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 257, 691, 862 is 1.

HCF(257, 691, 862) = 1

HCF of 257, 691, 862 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 257, 691, 862 is 1.

Highest Common Factor of 257,691,862 using Euclid's algorithm

Highest Common Factor of 257,691,862 is 1

Step 1: Since 691 > 257, we apply the division lemma to 691 and 257, to get

691 = 257 x 2 + 177

Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 177 and 257, to get

257 = 177 x 1 + 80

Step 3: We consider the new divisor 177 and the new remainder 80, and apply the division lemma to get

177 = 80 x 2 + 17

We consider the new divisor 80 and the new remainder 17,and apply the division lemma to get

80 = 17 x 4 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 257 and 691 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(80,17) = HCF(177,80) = HCF(257,177) = HCF(691,257) .

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

Step 1: Since 862 > 1, we apply the division lemma to 862 and 1, to get

862 = 1 x 862 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 862 is 1

Notice that 1 = HCF(862,1) .

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Frequently Asked Questions on HCF of 257, 691, 862 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 257, 691, 862?

Answer: HCF of 257, 691, 862 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 257, 691, 862 using Euclid's Algorithm?

Answer: For arbitrary numbers 257, 691, 862 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.