Highest Common Factor of 869, 682, 135 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 869, 682, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 869, 682, 135 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 869, 682, 135 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 869, 682, 135 is 1.

HCF(869, 682, 135) = 1

HCF of 869, 682, 135 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 869, 682, 135 is 1.

Highest Common Factor of 869,682,135 using Euclid's algorithm

Highest Common Factor of 869,682,135 is 1

Step 1: Since 869 > 682, we apply the division lemma to 869 and 682, to get

869 = 682 x 1 + 187

Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 187 and 682, to get

682 = 187 x 3 + 121

Step 3: We consider the new divisor 187 and the new remainder 121, and apply the division lemma to get

187 = 121 x 1 + 66

We consider the new divisor 121 and the new remainder 66,and apply the division lemma to get

121 = 66 x 1 + 55

We consider the new divisor 66 and the new remainder 55,and apply the division lemma to get

66 = 55 x 1 + 11

We consider the new divisor 55 and the new remainder 11,and apply the division lemma to get

55 = 11 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 869 and 682 is 11

Notice that 11 = HCF(55,11) = HCF(66,55) = HCF(121,66) = HCF(187,121) = HCF(682,187) = HCF(869,682) .

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

Step 1: Since 135 > 11, we apply the division lemma to 135 and 11, to get

135 = 11 x 12 + 3

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 3 and 11, to get

11 = 3 x 3 + 2

Step 3: 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 11 and 135 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(135,11) .

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Frequently Asked Questions on HCF of 869, 682, 135 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 869, 682, 135?

Answer: HCF of 869, 682, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 869, 682, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 869, 682, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.