Highest Common Factor of 608, 771, 723 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 608, 771, 723 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 608, 771, 723 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 608, 771, 723 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 608, 771, 723 is 1.

HCF(608, 771, 723) = 1

HCF of 608, 771, 723 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 608, 771, 723 is 1.

Highest Common Factor of 608,771,723 using Euclid's algorithm

Highest Common Factor of 608,771,723 is 1

Step 1: Since 771 > 608, we apply the division lemma to 771 and 608, to get

771 = 608 x 1 + 163

Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 163 and 608, to get

608 = 163 x 3 + 119

Step 3: We consider the new divisor 163 and the new remainder 119, and apply the division lemma to get

163 = 119 x 1 + 44

We consider the new divisor 119 and the new remainder 44,and apply the division lemma to get

119 = 44 x 2 + 31

We consider the new divisor 44 and the new remainder 31,and apply the division lemma to get

44 = 31 x 1 + 13

We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get

31 = 13 x 2 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 608 and 771 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(44,31) = HCF(119,44) = HCF(163,119) = HCF(608,163) = HCF(771,608) .

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

Step 1: Since 723 > 1, we apply the division lemma to 723 and 1, to get

723 = 1 x 723 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 723 is 1

Notice that 1 = HCF(723,1) .

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Frequently Asked Questions on HCF of 608, 771, 723 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 608, 771, 723?

Answer: HCF of 608, 771, 723 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 608, 771, 723 using Euclid's Algorithm?

Answer: For arbitrary numbers 608, 771, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.