Highest Common Factor of 865, 312, 73 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 865, 312, 73 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 865, 312, 73 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 865, 312, 73 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 865, 312, 73 is 1.

HCF(865, 312, 73) = 1

HCF of 865, 312, 73 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 865, 312, 73 is 1.

Highest Common Factor of 865,312,73 using Euclid's algorithm

Highest Common Factor of 865,312,73 is 1

Step 1: Since 865 > 312, we apply the division lemma to 865 and 312, to get

865 = 312 x 2 + 241

Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 241 and 312, to get

312 = 241 x 1 + 71

Step 3: We consider the new divisor 241 and the new remainder 71, and apply the division lemma to get

241 = 71 x 3 + 28

We consider the new divisor 71 and the new remainder 28,and apply the division lemma to get

71 = 28 x 2 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 865 and 312 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(71,28) = HCF(241,71) = HCF(312,241) = HCF(865,312) .

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

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

73 = 1 x 73 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 73 is 1

Notice that 1 = HCF(73,1) .

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Frequently Asked Questions on HCF of 865, 312, 73 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 865, 312, 73?

Answer: HCF of 865, 312, 73 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 865, 312, 73 using Euclid's Algorithm?

Answer: For arbitrary numbers 865, 312, 73 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.