Highest Common Factor of 365, 999, 872 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, 999, 872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 365, 999, 872 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, 999, 872 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, 999, 872 is 1.

HCF(365, 999, 872) = 1

HCF of 365, 999, 872 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, 999, 872 is 1.

Highest Common Factor of 365,999,872 using Euclid's algorithm

Highest Common Factor of 365,999,872 is 1

Step 1: Since 999 > 365, we apply the division lemma to 999 and 365, to get

999 = 365 x 2 + 269

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 269 and 365, to get

365 = 269 x 1 + 96

Step 3: We consider the new divisor 269 and the new remainder 96, and apply the division lemma to get

269 = 96 x 2 + 77

We consider the new divisor 96 and the new remainder 77,and apply the division lemma to get

96 = 77 x 1 + 19

We consider the new divisor 77 and the new remainder 19,and apply the division lemma to get

77 = 19 x 4 + 1

We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 365 and 999 is 1

Notice that 1 = HCF(19,1) = HCF(77,19) = HCF(96,77) = HCF(269,96) = HCF(365,269) = HCF(999,365) .

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

Step 1: Since 872 > 1, we apply the division lemma to 872 and 1, to get

872 = 1 x 872 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 872 is 1

Notice that 1 = HCF(872,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 365, 999, 872 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, 999, 872?

Answer: HCF of 365, 999, 872 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 365, 999, 872 using Euclid's Algorithm?

Answer: For arbitrary numbers 365, 999, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.