Highest Common Factor of 8345, 9634, 27416 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 8345, 9634, 27416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8345, 9634, 27416 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 8345, 9634, 27416 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 8345, 9634, 27416 is 1.

HCF(8345, 9634, 27416) = 1

HCF of 8345, 9634, 27416 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 8345, 9634, 27416 is 1.

Highest Common Factor of 8345,9634,27416 using Euclid's algorithm

Highest Common Factor of 8345,9634,27416 is 1

Step 1: Since 9634 > 8345, we apply the division lemma to 9634 and 8345, to get

9634 = 8345 x 1 + 1289

Step 2: Since the reminder 8345 ≠ 0, we apply division lemma to 1289 and 8345, to get

8345 = 1289 x 6 + 611

Step 3: We consider the new divisor 1289 and the new remainder 611, and apply the division lemma to get

1289 = 611 x 2 + 67

We consider the new divisor 611 and the new remainder 67,and apply the division lemma to get

611 = 67 x 9 + 8

We consider the new divisor 67 and the new remainder 8,and apply the division lemma to get

67 = 8 x 8 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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 8345 and 9634 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(67,8) = HCF(611,67) = HCF(1289,611) = HCF(8345,1289) = HCF(9634,8345) .

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

Step 1: Since 27416 > 1, we apply the division lemma to 27416 and 1, to get

27416 = 1 x 27416 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27416 is 1

Notice that 1 = HCF(27416,1) .

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Frequently Asked Questions on HCF of 8345, 9634, 27416 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 8345, 9634, 27416?

Answer: HCF of 8345, 9634, 27416 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8345, 9634, 27416 using Euclid's Algorithm?

Answer: For arbitrary numbers 8345, 9634, 27416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.