Highest Common Factor of 654, 831, 860 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 654, 831, 860 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 654, 831, 860 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 654, 831, 860 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 654, 831, 860 is 1.

HCF(654, 831, 860) = 1

HCF of 654, 831, 860 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 654, 831, 860 is 1.

Highest Common Factor of 654,831,860 using Euclid's algorithm

Highest Common Factor of 654,831,860 is 1

Step 1: Since 831 > 654, we apply the division lemma to 831 and 654, to get

831 = 654 x 1 + 177

Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 177 and 654, to get

654 = 177 x 3 + 123

Step 3: We consider the new divisor 177 and the new remainder 123, and apply the division lemma to get

177 = 123 x 1 + 54

We consider the new divisor 123 and the new remainder 54,and apply the division lemma to get

123 = 54 x 2 + 15

We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get

54 = 15 x 3 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 654 and 831 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(123,54) = HCF(177,123) = HCF(654,177) = HCF(831,654) .

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

Step 1: Since 860 > 3, we apply the division lemma to 860 and 3, to get

860 = 3 x 286 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 860 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(860,3) .

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Frequently Asked Questions on HCF of 654, 831, 860 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 654, 831, 860?

Answer: HCF of 654, 831, 860 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 654, 831, 860 using Euclid's Algorithm?

Answer: For arbitrary numbers 654, 831, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.