Highest Common Factor of 185, 515, 229 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 185, 515, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 185, 515, 229 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 185, 515, 229 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 185, 515, 229 is 1.

HCF(185, 515, 229) = 1

HCF of 185, 515, 229 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 185, 515, 229 is 1.

Highest Common Factor of 185,515,229 using Euclid's algorithm

Highest Common Factor of 185,515,229 is 1

Step 1: Since 515 > 185, we apply the division lemma to 515 and 185, to get

515 = 185 x 2 + 145

Step 2: Since the reminder 185 ≠ 0, we apply division lemma to 145 and 185, to get

185 = 145 x 1 + 40

Step 3: We consider the new divisor 145 and the new remainder 40, and apply the division lemma to get

145 = 40 x 3 + 25

We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get

40 = 25 x 1 + 15

We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get

25 = 15 x 1 + 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 185 and 515 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(145,40) = HCF(185,145) = HCF(515,185) .

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

Step 1: Since 229 > 5, we apply the division lemma to 229 and 5, to get

229 = 5 x 45 + 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 229 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(229,5) .

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Frequently Asked Questions on HCF of 185, 515, 229 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 185, 515, 229?

Answer: HCF of 185, 515, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 185, 515, 229 using Euclid's Algorithm?

Answer: For arbitrary numbers 185, 515, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.