Highest Common Factor of 197, 116, 122 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 197, 116, 122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 197, 116, 122 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 197, 116, 122 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 197, 116, 122 is 1.

HCF(197, 116, 122) = 1

HCF of 197, 116, 122 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 197, 116, 122 is 1.

Highest Common Factor of 197,116,122 using Euclid's algorithm

Highest Common Factor of 197,116,122 is 1

Step 1: Since 197 > 116, we apply the division lemma to 197 and 116, to get

197 = 116 x 1 + 81

Step 2: Since the reminder 116 ≠ 0, we apply division lemma to 81 and 116, to get

116 = 81 x 1 + 35

Step 3: We consider the new divisor 81 and the new remainder 35, and apply the division lemma to get

81 = 35 x 2 + 11

We consider the new divisor 35 and the new remainder 11,and apply the division lemma to get

35 = 11 x 3 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 197 and 116 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(81,35) = HCF(116,81) = HCF(197,116) .

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

Step 1: Since 122 > 1, we apply the division lemma to 122 and 1, to get

122 = 1 x 122 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 122 is 1

Notice that 1 = HCF(122,1) .

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Frequently Asked Questions on HCF of 197, 116, 122 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 197, 116, 122?

Answer: HCF of 197, 116, 122 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 197, 116, 122 using Euclid's Algorithm?

Answer: For arbitrary numbers 197, 116, 122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.