Highest Common Factor of 857, 992, 914 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 857, 992, 914 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 857, 992, 914 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 857, 992, 914 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 857, 992, 914 is 1.

HCF(857, 992, 914) = 1

HCF of 857, 992, 914 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 857, 992, 914 is 1.

Highest Common Factor of 857,992,914 using Euclid's algorithm

Highest Common Factor of 857,992,914 is 1

Step 1: Since 992 > 857, we apply the division lemma to 992 and 857, to get

992 = 857 x 1 + 135

Step 2: Since the reminder 857 ≠ 0, we apply division lemma to 135 and 857, to get

857 = 135 x 6 + 47

Step 3: We consider the new divisor 135 and the new remainder 47, and apply the division lemma to get

135 = 47 x 2 + 41

We consider the new divisor 47 and the new remainder 41,and apply the division lemma to get

47 = 41 x 1 + 6

We consider the new divisor 41 and the new remainder 6,and apply the division lemma to get

41 = 6 x 6 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 992 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(41,6) = HCF(47,41) = HCF(135,47) = HCF(857,135) = HCF(992,857) .

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

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

914 = 1 x 914 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 914 is 1

Notice that 1 = HCF(914,1) .

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Frequently Asked Questions on HCF of 857, 992, 914 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 857, 992, 914?

Answer: HCF of 857, 992, 914 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 857, 992, 914 using Euclid's Algorithm?

Answer: For arbitrary numbers 857, 992, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.