Highest Common Factor of 364, 663, 350 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 364, 663, 350 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 364, 663, 350 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 364, 663, 350 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 364, 663, 350 is 1.

HCF(364, 663, 350) = 1

HCF of 364, 663, 350 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 364, 663, 350 is 1.

Highest Common Factor of 364,663,350 using Euclid's algorithm

Highest Common Factor of 364,663,350 is 1

Step 1: Since 663 > 364, we apply the division lemma to 663 and 364, to get

663 = 364 x 1 + 299

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 299 and 364, to get

364 = 299 x 1 + 65

Step 3: We consider the new divisor 299 and the new remainder 65, and apply the division lemma to get

299 = 65 x 4 + 39

We consider the new divisor 65 and the new remainder 39,and apply the division lemma to get

65 = 39 x 1 + 26

We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get

39 = 26 x 1 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 364 and 663 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(65,39) = HCF(299,65) = HCF(364,299) = HCF(663,364) .

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

Step 1: Since 350 > 13, we apply the division lemma to 350 and 13, to get

350 = 13 x 26 + 12

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 12 and 13, to get

13 = 12 x 1 + 1

Step 3: We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 350 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(350,13) .

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Frequently Asked Questions on HCF of 364, 663, 350 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 364, 663, 350?

Answer: HCF of 364, 663, 350 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 364, 663, 350 using Euclid's Algorithm?

Answer: For arbitrary numbers 364, 663, 350 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.