Highest Common Factor of 861, 239, 141 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 861, 239, 141 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 861, 239, 141 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 861, 239, 141 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 861, 239, 141 is 1.

HCF(861, 239, 141) = 1

HCF of 861, 239, 141 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 861, 239, 141 is 1.

Highest Common Factor of 861,239,141 using Euclid's algorithm

Highest Common Factor of 861,239,141 is 1

Step 1: Since 861 > 239, we apply the division lemma to 861 and 239, to get

861 = 239 x 3 + 144

Step 2: Since the reminder 239 ≠ 0, we apply division lemma to 144 and 239, to get

239 = 144 x 1 + 95

Step 3: We consider the new divisor 144 and the new remainder 95, and apply the division lemma to get

144 = 95 x 1 + 49

We consider the new divisor 95 and the new remainder 49,and apply the division lemma to get

95 = 49 x 1 + 46

We consider the new divisor 49 and the new remainder 46,and apply the division lemma to get

49 = 46 x 1 + 3

We consider the new divisor 46 and the new remainder 3,and apply the division lemma to get

46 = 3 x 15 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 861 and 239 is 1

Notice that 1 = HCF(3,1) = HCF(46,3) = HCF(49,46) = HCF(95,49) = HCF(144,95) = HCF(239,144) = HCF(861,239) .

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

Step 1: Since 141 > 1, we apply the division lemma to 141 and 1, to get

141 = 1 x 141 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 141 is 1

Notice that 1 = HCF(141,1) .

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Frequently Asked Questions on HCF of 861, 239, 141 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 861, 239, 141?

Answer: HCF of 861, 239, 141 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 861, 239, 141 using Euclid's Algorithm?

Answer: For arbitrary numbers 861, 239, 141 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.