Highest Common Factor of 91, 65, 73, 40 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 91, 65, 73, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 91, 65, 73, 40 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 91, 65, 73, 40 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 91, 65, 73, 40 is 1.

HCF(91, 65, 73, 40) = 1

HCF of 91, 65, 73, 40 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 91, 65, 73, 40 is 1.

Highest Common Factor of 91,65,73,40 using Euclid's algorithm

Highest Common Factor of 91,65,73,40 is 1

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 91 and 65 is 13

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

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

Step 1: Since 73 > 13, we apply the division lemma to 73 and 13, to get

73 = 13 x 5 + 8

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get

13 = 8 x 1 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 13 and 73 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(73,13) .

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

Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get

40 = 1 x 40 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1

Notice that 1 = HCF(40,1) .

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Frequently Asked Questions on HCF of 91, 65, 73, 40 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 91, 65, 73, 40?

Answer: HCF of 91, 65, 73, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 91, 65, 73, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 91, 65, 73, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.