Highest Common Factor of 914, 559, 777 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 914, 559, 777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 914, 559, 777 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 914, 559, 777 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 914, 559, 777 is 1.

HCF(914, 559, 777) = 1

HCF of 914, 559, 777 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 914, 559, 777 is 1.

Highest Common Factor of 914,559,777 using Euclid's algorithm

Highest Common Factor of 914,559,777 is 1

Step 1: Since 914 > 559, we apply the division lemma to 914 and 559, to get

914 = 559 x 1 + 355

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 355 and 559, to get

559 = 355 x 1 + 204

Step 3: We consider the new divisor 355 and the new remainder 204, and apply the division lemma to get

355 = 204 x 1 + 151

We consider the new divisor 204 and the new remainder 151,and apply the division lemma to get

204 = 151 x 1 + 53

We consider the new divisor 151 and the new remainder 53,and apply the division lemma to get

151 = 53 x 2 + 45

We consider the new divisor 53 and the new remainder 45,and apply the division lemma to get

53 = 45 x 1 + 8

We consider the new divisor 45 and the new remainder 8,and apply the division lemma to get

45 = 8 x 5 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 914 and 559 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(45,8) = HCF(53,45) = HCF(151,53) = HCF(204,151) = HCF(355,204) = HCF(559,355) = HCF(914,559) .


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

Step 1: Since 777 > 1, we apply the division lemma to 777 and 1, to get

777 = 1 x 777 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 777 is 1

Notice that 1 = HCF(777,1) .

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Frequently Asked Questions on HCF of 914, 559, 777 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 914, 559, 777?

Answer: HCF of 914, 559, 777 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 914, 559, 777 using Euclid's Algorithm?

Answer: For arbitrary numbers 914, 559, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.