Highest Common Factor of 678, 416, 207 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, 416, 207 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 678, 416, 207 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, 416, 207 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, 416, 207 is 1.

HCF(678, 416, 207) = 1

HCF of 678, 416, 207 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, 416, 207 is 1.

Highest Common Factor of 678,416,207 using Euclid's algorithm

Highest Common Factor of 678,416,207 is 1

Step 1: Since 678 > 416, we apply the division lemma to 678 and 416, to get

678 = 416 x 1 + 262

Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 262 and 416, to get

416 = 262 x 1 + 154

Step 3: We consider the new divisor 262 and the new remainder 154, and apply the division lemma to get

262 = 154 x 1 + 108

We consider the new divisor 154 and the new remainder 108,and apply the division lemma to get

154 = 108 x 1 + 46

We consider the new divisor 108 and the new remainder 46,and apply the division lemma to get

108 = 46 x 2 + 16

We consider the new divisor 46 and the new remainder 16,and apply the division lemma to get

46 = 16 x 2 + 14

We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get

16 = 14 x 1 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 416 is 2

Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(46,16) = HCF(108,46) = HCF(154,108) = HCF(262,154) = HCF(416,262) = HCF(678,416) .

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

Step 1: Since 207 > 2, we apply the division lemma to 207 and 2, to get

207 = 2 x 103 + 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 207 is 1

Notice that 1 = HCF(2,1) = HCF(207,2) .

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Frequently Asked Questions on HCF of 678, 416, 207 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, 416, 207?

Answer: HCF of 678, 416, 207 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 678, 416, 207 using Euclid's Algorithm?

Answer: For arbitrary numbers 678, 416, 207 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.