Highest Common Factor of 264, 294, 317 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 264, 294, 317 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 264, 294, 317 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 264, 294, 317 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 264, 294, 317 is 1.

HCF(264, 294, 317) = 1

HCF of 264, 294, 317 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 264, 294, 317 is 1.

Highest Common Factor of 264,294,317 using Euclid's algorithm

Highest Common Factor of 264,294,317 is 1

Step 1: Since 294 > 264, we apply the division lemma to 294 and 264, to get

294 = 264 x 1 + 30

Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 30 and 264, to get

264 = 30 x 8 + 24

Step 3: We consider the new divisor 30 and the new remainder 24, and apply the division lemma to get

30 = 24 x 1 + 6

We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get

24 = 6 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 264 and 294 is 6

Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(264,30) = HCF(294,264) .

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

Step 1: Since 317 > 6, we apply the division lemma to 317 and 6, to get

317 = 6 x 52 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 317 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(317,6) .

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Frequently Asked Questions on HCF of 264, 294, 317 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 264, 294, 317?

Answer: HCF of 264, 294, 317 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 264, 294, 317 using Euclid's Algorithm?

Answer: For arbitrary numbers 264, 294, 317 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.