Highest Common Factor of 65, 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 65, 91 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 65, 91 is 13 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 65, 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 65, 91 is 13.

HCF(65, 91) = 13

HCF of 65, 91 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 65, 91 is 13.

Highest Common Factor of 65,91 using Euclid's algorithm

Highest Common Factor of 65,91 is 13

Step 1: Since 91 > 65, we apply the division lemma to 91 and 65, to get

91 = 65 x 1 + 26

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 26 and 65, to get

65 = 26 x 2 + 13

Step 3: We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 65 and 91 is 13

Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(91,65) .

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Frequently Asked Questions on HCF of 65, 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 65, 91?

Answer: HCF of 65, 91 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 65, 91 using Euclid's Algorithm?

Answer: For arbitrary numbers 65, 91 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.