Highest Common Factor of 878, 331, 857 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 878, 331, 857 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 878, 331, 857 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 878, 331, 857 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 878, 331, 857 is 1.

HCF(878, 331, 857) = 1

HCF of 878, 331, 857 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 878, 331, 857 is 1.

Highest Common Factor of 878,331,857 using Euclid's algorithm

Highest Common Factor of 878,331,857 is 1

Step 1: Since 878 > 331, we apply the division lemma to 878 and 331, to get

878 = 331 x 2 + 216

Step 2: Since the reminder 331 ≠ 0, we apply division lemma to 216 and 331, to get

331 = 216 x 1 + 115

Step 3: We consider the new divisor 216 and the new remainder 115, and apply the division lemma to get

216 = 115 x 1 + 101

We consider the new divisor 115 and the new remainder 101,and apply the division lemma to get

115 = 101 x 1 + 14

We consider the new divisor 101 and the new remainder 14,and apply the division lemma to get

101 = 14 x 7 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 878 and 331 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(101,14) = HCF(115,101) = HCF(216,115) = HCF(331,216) = HCF(878,331) .

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

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

857 = 1 x 857 + 0

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

Notice that 1 = HCF(857,1) .

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Frequently Asked Questions on HCF of 878, 331, 857 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 878, 331, 857?

Answer: HCF of 878, 331, 857 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 878, 331, 857 using Euclid's Algorithm?

Answer: For arbitrary numbers 878, 331, 857 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.