Highest Common Factor of 854, 909, 770 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 854, 909, 770 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 909, 770 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 854, 909, 770 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 854, 909, 770 is 1.

HCF(854, 909, 770) = 1

HCF of 854, 909, 770 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 854, 909, 770 is 1.

Highest Common Factor of 854,909,770 using Euclid's algorithm

Highest Common Factor of 854,909,770 is 1

Step 1: Since 909 > 854, we apply the division lemma to 909 and 854, to get

909 = 854 x 1 + 55

Step 2: Since the reminder 854 ≠ 0, we apply division lemma to 55 and 854, to get

854 = 55 x 15 + 29

Step 3: We consider the new divisor 55 and the new remainder 29, and apply the division lemma to get

55 = 29 x 1 + 26

We consider the new divisor 29 and the new remainder 26,and apply the division lemma to get

29 = 26 x 1 + 3

We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get

26 = 3 x 8 + 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 854 and 909 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(29,26) = HCF(55,29) = HCF(854,55) = HCF(909,854) .

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

Step 1: Since 770 > 1, we apply the division lemma to 770 and 1, to get

770 = 1 x 770 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 770 is 1

Notice that 1 = HCF(770,1) .

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Frequently Asked Questions on HCF of 854, 909, 770 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 854, 909, 770?

Answer: HCF of 854, 909, 770 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 909, 770 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 909, 770 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.