Highest Common Factor of 310, 502, 323 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, 502, 323 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 502, 323 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, 502, 323 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, 502, 323 is 1.

HCF(310, 502, 323) = 1

HCF of 310, 502, 323 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, 502, 323 is 1.

Highest Common Factor of 310,502,323 using Euclid's algorithm

Highest Common Factor of 310,502,323 is 1

Step 1: Since 502 > 310, we apply the division lemma to 502 and 310, to get

502 = 310 x 1 + 192

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 192 and 310, to get

310 = 192 x 1 + 118

Step 3: We consider the new divisor 192 and the new remainder 118, and apply the division lemma to get

192 = 118 x 1 + 74

We consider the new divisor 118 and the new remainder 74,and apply the division lemma to get

118 = 74 x 1 + 44

We consider the new divisor 74 and the new remainder 44,and apply the division lemma to get

74 = 44 x 1 + 30

We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get

44 = 30 x 1 + 14

We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get

30 = 14 x 2 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 502 is 2

Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(74,44) = HCF(118,74) = HCF(192,118) = HCF(310,192) = HCF(502,310) .

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

Step 1: Since 323 > 2, we apply the division lemma to 323 and 2, to get

323 = 2 x 161 + 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 323 is 1

Notice that 1 = HCF(2,1) = HCF(323,2) .

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Frequently Asked Questions on HCF of 310, 502, 323 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, 502, 323?

Answer: HCF of 310, 502, 323 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 502, 323 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 502, 323 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.