Highest Common Factor of 469, 766, 666 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 469, 766, 666 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 469, 766, 666 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 469, 766, 666 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 469, 766, 666 is 1.

HCF(469, 766, 666) = 1

HCF of 469, 766, 666 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 469, 766, 666 is 1.

Highest Common Factor of 469,766,666 using Euclid's algorithm

Highest Common Factor of 469,766,666 is 1

Step 1: Since 766 > 469, we apply the division lemma to 766 and 469, to get

766 = 469 x 1 + 297

Step 2: Since the reminder 469 ≠ 0, we apply division lemma to 297 and 469, to get

469 = 297 x 1 + 172

Step 3: We consider the new divisor 297 and the new remainder 172, and apply the division lemma to get

297 = 172 x 1 + 125

We consider the new divisor 172 and the new remainder 125,and apply the division lemma to get

172 = 125 x 1 + 47

We consider the new divisor 125 and the new remainder 47,and apply the division lemma to get

125 = 47 x 2 + 31

We consider the new divisor 47 and the new remainder 31,and apply the division lemma to get

47 = 31 x 1 + 16

We consider the new divisor 31 and the new remainder 16,and apply the division lemma to get

31 = 16 x 1 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 469 and 766 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(31,16) = HCF(47,31) = HCF(125,47) = HCF(172,125) = HCF(297,172) = HCF(469,297) = HCF(766,469) .

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

Step 1: Since 666 > 1, we apply the division lemma to 666 and 1, to get

666 = 1 x 666 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 666 is 1

Notice that 1 = HCF(666,1) .

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Frequently Asked Questions on HCF of 469, 766, 666 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 469, 766, 666?

Answer: HCF of 469, 766, 666 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 469, 766, 666 using Euclid's Algorithm?

Answer: For arbitrary numbers 469, 766, 666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.