Highest Common Factor of 677, 235, 107 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 677, 235, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 677, 235, 107 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 677, 235, 107 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 677, 235, 107 is 1.

HCF(677, 235, 107) = 1

HCF of 677, 235, 107 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 677, 235, 107 is 1.

Highest Common Factor of 677,235,107 using Euclid's algorithm

Highest Common Factor of 677,235,107 is 1

Step 1: Since 677 > 235, we apply the division lemma to 677 and 235, to get

677 = 235 x 2 + 207

Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 207 and 235, to get

235 = 207 x 1 + 28

Step 3: We consider the new divisor 207 and the new remainder 28, and apply the division lemma to get

207 = 28 x 7 + 11

We consider the new divisor 28 and the new remainder 11,and apply the division lemma to get

28 = 11 x 2 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 677 and 235 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(28,11) = HCF(207,28) = HCF(235,207) = HCF(677,235) .

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

Step 1: Since 107 > 1, we apply the division lemma to 107 and 1, to get

107 = 1 x 107 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 107 is 1

Notice that 1 = HCF(107,1) .

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Frequently Asked Questions on HCF of 677, 235, 107 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 677, 235, 107?

Answer: HCF of 677, 235, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 677, 235, 107 using Euclid's Algorithm?

Answer: For arbitrary numbers 677, 235, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.