Highest Common Factor of 709, 816, 91 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 709, 816, 91 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 709, 816, 91 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 709, 816, 91 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 709, 816, 91 is 1.

HCF(709, 816, 91) = 1

HCF of 709, 816, 91 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 709, 816, 91 is 1.

Highest Common Factor of 709,816,91 using Euclid's algorithm

Highest Common Factor of 709,816,91 is 1

Step 1: Since 816 > 709, we apply the division lemma to 816 and 709, to get

816 = 709 x 1 + 107

Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 107 and 709, to get

709 = 107 x 6 + 67

Step 3: We consider the new divisor 107 and the new remainder 67, and apply the division lemma to get

107 = 67 x 1 + 40

We consider the new divisor 67 and the new remainder 40,and apply the division lemma to get

67 = 40 x 1 + 27

We consider the new divisor 40 and the new remainder 27,and apply the division lemma to get

40 = 27 x 1 + 13

We consider the new divisor 27 and the new remainder 13,and apply the division lemma to get

27 = 13 x 2 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 816 is 1

Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(40,27) = HCF(67,40) = HCF(107,67) = HCF(709,107) = HCF(816,709) .

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

Step 1: Since 91 > 1, we apply the division lemma to 91 and 1, to get

91 = 1 x 91 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 91 is 1

Notice that 1 = HCF(91,1) .

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Frequently Asked Questions on HCF of 709, 816, 91 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 709, 816, 91?

Answer: HCF of 709, 816, 91 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 709, 816, 91 using Euclid's Algorithm?

Answer: For arbitrary numbers 709, 816, 91 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.