Highest Common Factor of 266, 701, 669 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 266, 701, 669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 266, 701, 669 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 266, 701, 669 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 266, 701, 669 is 1.

HCF(266, 701, 669) = 1

HCF of 266, 701, 669 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 266, 701, 669 is 1.

Highest Common Factor of 266,701,669 using Euclid's algorithm

Highest Common Factor of 266,701,669 is 1

Step 1: Since 701 > 266, we apply the division lemma to 701 and 266, to get

701 = 266 x 2 + 169

Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 169 and 266, to get

266 = 169 x 1 + 97

Step 3: We consider the new divisor 169 and the new remainder 97, and apply the division lemma to get

169 = 97 x 1 + 72

We consider the new divisor 97 and the new remainder 72,and apply the division lemma to get

97 = 72 x 1 + 25

We consider the new divisor 72 and the new remainder 25,and apply the division lemma to get

72 = 25 x 2 + 22

We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get

25 = 22 x 1 + 3

We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get

22 = 3 x 7 + 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 266 and 701 is 1

Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(72,25) = HCF(97,72) = HCF(169,97) = HCF(266,169) = HCF(701,266) .

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

Step 1: Since 669 > 1, we apply the division lemma to 669 and 1, to get

669 = 1 x 669 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1

Notice that 1 = HCF(669,1) .

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Frequently Asked Questions on HCF of 266, 701, 669 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 266, 701, 669?

Answer: HCF of 266, 701, 669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 266, 701, 669 using Euclid's Algorithm?

Answer: For arbitrary numbers 266, 701, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.