Highest Common Factor of 266, 697, 489, 670 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, 697, 489, 670 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 266, 697, 489, 670 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, 697, 489, 670 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, 697, 489, 670 is 1.

HCF(266, 697, 489, 670) = 1

HCF of 266, 697, 489, 670 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, 697, 489, 670 is 1.

Highest Common Factor of 266,697,489,670 using Euclid's algorithm

Highest Common Factor of 266,697,489,670 is 1

Step 1: Since 697 > 266, we apply the division lemma to 697 and 266, to get

697 = 266 x 2 + 165

Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 165 and 266, to get

266 = 165 x 1 + 101

Step 3: We consider the new divisor 165 and the new remainder 101, and apply the division lemma to get

165 = 101 x 1 + 64

We consider the new divisor 101 and the new remainder 64,and apply the division lemma to get

101 = 64 x 1 + 37

We consider the new divisor 64 and the new remainder 37,and apply the division lemma to get

64 = 37 x 1 + 27

We consider the new divisor 37 and the new remainder 27,and apply the division lemma to get

37 = 27 x 1 + 10

We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get

27 = 10 x 2 + 7

We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get

10 = 7 x 1 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 697 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(64,37) = HCF(101,64) = HCF(165,101) = HCF(266,165) = HCF(697,266) .

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

Step 1: Since 489 > 1, we apply the division lemma to 489 and 1, to get

489 = 1 x 489 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 489 is 1

Notice that 1 = HCF(489,1) .

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

Step 1: Since 670 > 1, we apply the division lemma to 670 and 1, to get

670 = 1 x 670 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 670 is 1

Notice that 1 = HCF(670,1) .

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Frequently Asked Questions on HCF of 266, 697, 489, 670 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, 697, 489, 670?

Answer: HCF of 266, 697, 489, 670 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 266, 697, 489, 670 using Euclid's Algorithm?

Answer: For arbitrary numbers 266, 697, 489, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.