Highest Common Factor of 771, 500, 301 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, 500, 301 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 771, 500, 301 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, 500, 301 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, 500, 301 is 1.

HCF(771, 500, 301) = 1

HCF of 771, 500, 301 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, 500, 301 is 1.

Highest Common Factor of 771,500,301 using Euclid's algorithm

Highest Common Factor of 771,500,301 is 1

Step 1: Since 771 > 500, we apply the division lemma to 771 and 500, to get

771 = 500 x 1 + 271

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 271 and 500, to get

500 = 271 x 1 + 229

Step 3: We consider the new divisor 271 and the new remainder 229, and apply the division lemma to get

271 = 229 x 1 + 42

We consider the new divisor 229 and the new remainder 42,and apply the division lemma to get

229 = 42 x 5 + 19

We consider the new divisor 42 and the new remainder 19,and apply the division lemma to get

42 = 19 x 2 + 4

We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get

19 = 4 x 4 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 771 and 500 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(42,19) = HCF(229,42) = HCF(271,229) = HCF(500,271) = HCF(771,500) .

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

Step 1: Since 301 > 1, we apply the division lemma to 301 and 1, to get

301 = 1 x 301 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 301 is 1

Notice that 1 = HCF(301,1) .

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Frequently Asked Questions on HCF of 771, 500, 301 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, 500, 301?

Answer: HCF of 771, 500, 301 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 771, 500, 301 using Euclid's Algorithm?

Answer: For arbitrary numbers 771, 500, 301 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.