Highest Common Factor of 691, 842, 209, 55 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 691, 842, 209, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 842, 209, 55 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 691, 842, 209, 55 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 691, 842, 209, 55 is 1.

HCF(691, 842, 209, 55) = 1

HCF of 691, 842, 209, 55 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 691, 842, 209, 55 is 1.

Highest Common Factor of 691,842,209,55 using Euclid's algorithm

Highest Common Factor of 691,842,209,55 is 1

Step 1: Since 842 > 691, we apply the division lemma to 842 and 691, to get

842 = 691 x 1 + 151

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 151 and 691, to get

691 = 151 x 4 + 87

Step 3: We consider the new divisor 151 and the new remainder 87, and apply the division lemma to get

151 = 87 x 1 + 64

We consider the new divisor 87 and the new remainder 64,and apply the division lemma to get

87 = 64 x 1 + 23

We consider the new divisor 64 and the new remainder 23,and apply the division lemma to get

64 = 23 x 2 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 691 and 842 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(64,23) = HCF(87,64) = HCF(151,87) = HCF(691,151) = HCF(842,691) .

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

Step 1: Since 209 > 1, we apply the division lemma to 209 and 1, to get

209 = 1 x 209 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 209 is 1

Notice that 1 = HCF(209,1) .

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

Step 1: Since 55 > 1, we apply the division lemma to 55 and 1, to get

55 = 1 x 55 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 55 is 1

Notice that 1 = HCF(55,1) .

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Frequently Asked Questions on HCF of 691, 842, 209, 55 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 691, 842, 209, 55?

Answer: HCF of 691, 842, 209, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 842, 209, 55 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 842, 209, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.