Highest Common Factor of 678, 927, 665 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 678, 927, 665 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 678, 927, 665 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 678, 927, 665 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 678, 927, 665 is 1.

HCF(678, 927, 665) = 1

HCF of 678, 927, 665 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 678, 927, 665 is 1.

Highest Common Factor of 678,927,665 using Euclid's algorithm

Highest Common Factor of 678,927,665 is 1

Step 1: Since 927 > 678, we apply the division lemma to 927 and 678, to get

927 = 678 x 1 + 249

Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 249 and 678, to get

678 = 249 x 2 + 180

Step 3: We consider the new divisor 249 and the new remainder 180, and apply the division lemma to get

249 = 180 x 1 + 69

We consider the new divisor 180 and the new remainder 69,and apply the division lemma to get

180 = 69 x 2 + 42

We consider the new divisor 69 and the new remainder 42,and apply the division lemma to get

69 = 42 x 1 + 27

We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get

42 = 27 x 1 + 15

We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get

27 = 15 x 1 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 678 and 927 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(69,42) = HCF(180,69) = HCF(249,180) = HCF(678,249) = HCF(927,678) .

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

Step 1: Since 665 > 3, we apply the division lemma to 665 and 3, to get

665 = 3 x 221 + 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 665 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(665,3) .

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Frequently Asked Questions on HCF of 678, 927, 665 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 678, 927, 665?

Answer: HCF of 678, 927, 665 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 678, 927, 665 using Euclid's Algorithm?

Answer: For arbitrary numbers 678, 927, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.