Highest Common Factor of 666, 808, 577 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, 808, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 666, 808, 577 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, 808, 577 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, 808, 577 is 1.

HCF(666, 808, 577) = 1

HCF of 666, 808, 577 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, 808, 577 is 1.

Highest Common Factor of 666,808,577 using Euclid's algorithm

Highest Common Factor of 666,808,577 is 1

Step 1: Since 808 > 666, we apply the division lemma to 808 and 666, to get

808 = 666 x 1 + 142

Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 142 and 666, to get

666 = 142 x 4 + 98

Step 3: We consider the new divisor 142 and the new remainder 98, and apply the division lemma to get

142 = 98 x 1 + 44

We consider the new divisor 98 and the new remainder 44,and apply the division lemma to get

98 = 44 x 2 + 10

We consider the new divisor 44 and the new remainder 10,and apply the division lemma to get

44 = 10 x 4 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 666 and 808 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(44,10) = HCF(98,44) = HCF(142,98) = HCF(666,142) = HCF(808,666) .

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

Step 1: Since 577 > 2, we apply the division lemma to 577 and 2, to get

577 = 2 x 288 + 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 577 is 1

Notice that 1 = HCF(2,1) = HCF(577,2) .

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Frequently Asked Questions on HCF of 666, 808, 577 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, 808, 577?

Answer: HCF of 666, 808, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 666, 808, 577 using Euclid's Algorithm?

Answer: For arbitrary numbers 666, 808, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.