Highest Common Factor of 171, 991, 266 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 171, 991, 266 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 171, 991, 266 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 171, 991, 266 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 171, 991, 266 is 1.

HCF(171, 991, 266) = 1

HCF of 171, 991, 266 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 171, 991, 266 is 1.

Highest Common Factor of 171,991,266 using Euclid's algorithm

Highest Common Factor of 171,991,266 is 1

Step 1: Since 991 > 171, we apply the division lemma to 991 and 171, to get

991 = 171 x 5 + 136

Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 136 and 171, to get

171 = 136 x 1 + 35

Step 3: We consider the new divisor 136 and the new remainder 35, and apply the division lemma to get

136 = 35 x 3 + 31

We consider the new divisor 35 and the new remainder 31,and apply the division lemma to get

35 = 31 x 1 + 4

We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get

31 = 4 x 7 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 171 and 991 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(35,31) = HCF(136,35) = HCF(171,136) = HCF(991,171) .

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

Step 1: Since 266 > 1, we apply the division lemma to 266 and 1, to get

266 = 1 x 266 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 266 is 1

Notice that 1 = HCF(266,1) .

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Frequently Asked Questions on HCF of 171, 991, 266 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 171, 991, 266?

Answer: HCF of 171, 991, 266 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 171, 991, 266 using Euclid's Algorithm?

Answer: For arbitrary numbers 171, 991, 266 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.