Highest Common Factor of 310, 596, 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 310, 596, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 596, 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 310, 596, 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 310, 596, 229 is 1.

HCF(310, 596, 229) = 1

HCF of 310, 596, 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 310, 596, 229 is 1.

Highest Common Factor of 310,596,229 using Euclid's algorithm

Highest Common Factor of 310,596,229 is 1

Step 1: Since 596 > 310, we apply the division lemma to 596 and 310, to get

596 = 310 x 1 + 286

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 286 and 310, to get

310 = 286 x 1 + 24

Step 3: We consider the new divisor 286 and the new remainder 24, and apply the division lemma to get

286 = 24 x 11 + 22

We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get

24 = 22 x 1 + 2

We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get

22 = 2 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 596 is 2

Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(286,24) = HCF(310,286) = HCF(596,310) .

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

Step 1: Since 229 > 2, we apply the division lemma to 229 and 2, to get

229 = 2 x 114 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 229 is 1

Notice that 1 = HCF(2,1) = HCF(229,2) .

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Frequently Asked Questions on HCF of 310, 596, 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 310, 596, 229?

Answer: HCF of 310, 596, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 596, 229 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 596, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.