Highest Common Factor of 771, 930, 508 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 771, 930, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 771, 930, 508 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 771, 930, 508 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 771, 930, 508 is 1.

HCF(771, 930, 508) = 1

HCF of 771, 930, 508 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 771, 930, 508 is 1.

Highest Common Factor of 771,930,508 using Euclid's algorithm

Highest Common Factor of 771,930,508 is 1

Step 1: Since 930 > 771, we apply the division lemma to 930 and 771, to get

930 = 771 x 1 + 159

Step 2: Since the reminder 771 ≠ 0, we apply division lemma to 159 and 771, to get

771 = 159 x 4 + 135

Step 3: We consider the new divisor 159 and the new remainder 135, and apply the division lemma to get

159 = 135 x 1 + 24

We consider the new divisor 135 and the new remainder 24,and apply the division lemma to get

135 = 24 x 5 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 771 and 930 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(135,24) = HCF(159,135) = HCF(771,159) = HCF(930,771) .

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

Step 1: Since 508 > 3, we apply the division lemma to 508 and 3, to get

508 = 3 x 169 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 508 is 1

Notice that 1 = HCF(3,1) = HCF(508,3) .

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Frequently Asked Questions on HCF of 771, 930, 508 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 771, 930, 508?

Answer: HCF of 771, 930, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 771, 930, 508 using Euclid's Algorithm?

Answer: For arbitrary numbers 771, 930, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.