Highest Common Factor of 508, 291, 14 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 508, 291, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 508, 291, 14 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 508, 291, 14 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 508, 291, 14 is 1.

HCF(508, 291, 14) = 1

HCF of 508, 291, 14 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 508, 291, 14 is 1.

Highest Common Factor of 508,291,14 using Euclid's algorithm

Highest Common Factor of 508,291,14 is 1

Step 1: Since 508 > 291, we apply the division lemma to 508 and 291, to get

508 = 291 x 1 + 217

Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 217 and 291, to get

291 = 217 x 1 + 74

Step 3: We consider the new divisor 217 and the new remainder 74, and apply the division lemma to get

217 = 74 x 2 + 69

We consider the new divisor 74 and the new remainder 69,and apply the division lemma to get

74 = 69 x 1 + 5

We consider the new divisor 69 and the new remainder 5,and apply the division lemma to get

69 = 5 x 13 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

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 508 and 291 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(69,5) = HCF(74,69) = HCF(217,74) = HCF(291,217) = HCF(508,291) .

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

Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1

Notice that 1 = HCF(14,1) .

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Frequently Asked Questions on HCF of 508, 291, 14 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 508, 291, 14?

Answer: HCF of 508, 291, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 508, 291, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 508, 291, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.