Highest Common Factor of 878, 190, 159 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, 190, 159 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 878, 190, 159 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, 190, 159 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, 190, 159 is 1.

HCF(878, 190, 159) = 1

HCF of 878, 190, 159 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 878, 190, 159 is 1.

Highest Common Factor of 878,190,159 using Euclid's algorithm

Highest Common Factor of 878,190,159 is 1

Step 1: Since 878 > 190, we apply the division lemma to 878 and 190, to get

878 = 190 x 4 + 118

Step 2: Since the reminder 190 ≠ 0, we apply division lemma to 118 and 190, to get

190 = 118 x 1 + 72

Step 3: We consider the new divisor 118 and the new remainder 72, and apply the division lemma to get

118 = 72 x 1 + 46

We consider the new divisor 72 and the new remainder 46,and apply the division lemma to get

72 = 46 x 1 + 26

We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get

46 = 26 x 1 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 878 and 190 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(72,46) = HCF(118,72) = HCF(190,118) = HCF(878,190) .

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

Step 1: Since 159 > 2, we apply the division lemma to 159 and 2, to get

159 = 2 x 79 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 159 is 1

Notice that 1 = HCF(2,1) = HCF(159,2) .

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Frequently Asked Questions on HCF of 878, 190, 159 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, 190, 159?

Answer: HCF of 878, 190, 159 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 878, 190, 159 using Euclid's Algorithm?

Answer: For arbitrary numbers 878, 190, 159 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.