Highest Common Factor of 666, 434, 943 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 666, 434, 943 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 666, 434, 943 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 666, 434, 943 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 666, 434, 943 is 1.

HCF(666, 434, 943) = 1

HCF of 666, 434, 943 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 666, 434, 943 is 1.

Highest Common Factor of 666,434,943 using Euclid's algorithm

Highest Common Factor of 666,434,943 is 1

Step 1: Since 666 > 434, we apply the division lemma to 666 and 434, to get

666 = 434 x 1 + 232

Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 232 and 434, to get

434 = 232 x 1 + 202

Step 3: We consider the new divisor 232 and the new remainder 202, and apply the division lemma to get

232 = 202 x 1 + 30

We consider the new divisor 202 and the new remainder 30,and apply the division lemma to get

202 = 30 x 6 + 22

We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get

30 = 22 x 1 + 8

We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get

22 = 8 x 2 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 666 and 434 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(202,30) = HCF(232,202) = HCF(434,232) = HCF(666,434) .

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

Step 1: Since 943 > 2, we apply the division lemma to 943 and 2, to get

943 = 2 x 471 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 943 is 1

Notice that 1 = HCF(2,1) = HCF(943,2) .

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Frequently Asked Questions on HCF of 666, 434, 943 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 666, 434, 943?

Answer: HCF of 666, 434, 943 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 666, 434, 943 using Euclid's Algorithm?

Answer: For arbitrary numbers 666, 434, 943 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.