Highest Common Factor of 365, 920, 874 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, 920, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 365, 920, 874 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, 920, 874 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, 920, 874 is 1.

HCF(365, 920, 874) = 1

HCF of 365, 920, 874 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, 920, 874 is 1.

Highest Common Factor of 365,920,874 using Euclid's algorithm

Highest Common Factor of 365,920,874 is 1

Step 1: Since 920 > 365, we apply the division lemma to 920 and 365, to get

920 = 365 x 2 + 190

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 190 and 365, to get

365 = 190 x 1 + 175

Step 3: We consider the new divisor 190 and the new remainder 175, and apply the division lemma to get

190 = 175 x 1 + 15

We consider the new divisor 175 and the new remainder 15,and apply the division lemma to get

175 = 15 x 11 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 365 and 920 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(175,15) = HCF(190,175) = HCF(365,190) = HCF(920,365) .

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

Step 1: Since 874 > 5, we apply the division lemma to 874 and 5, to get

874 = 5 x 174 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 874 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(874,5) .

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, 920, 874 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, 920, 874?

Answer: HCF of 365, 920, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 365, 920, 874 using Euclid's Algorithm?

Answer: For arbitrary numbers 365, 920, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.