Highest Common Factor of 365, 873 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 365, 873 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 365, 873 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 365, 873 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 365, 873 is 1.

HCF(365, 873) = 1

HCF of 365, 873 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 365, 873 is 1.

Highest Common Factor of 365,873 using Euclid's algorithm

Highest Common Factor of 365,873 is 1

Step 1: Since 873 > 365, we apply the division lemma to 873 and 365, to get

873 = 365 x 2 + 143

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 143 and 365, to get

365 = 143 x 2 + 79

Step 3: We consider the new divisor 143 and the new remainder 79, and apply the division lemma to get

143 = 79 x 1 + 64

We consider the new divisor 79 and the new remainder 64,and apply the division lemma to get

79 = 64 x 1 + 15

We consider the new divisor 64 and the new remainder 15,and apply the division lemma to get

64 = 15 x 4 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 365 and 873 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(64,15) = HCF(79,64) = HCF(143,79) = HCF(365,143) = HCF(873,365) .

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Frequently Asked Questions on HCF of 365, 873 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 365, 873?

Answer: HCF of 365, 873 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 365, 873 using Euclid's Algorithm?

Answer: For arbitrary numbers 365, 873 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.