Highest Common Factor of 278, 617, 251 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 278, 617, 251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 278, 617, 251 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 278, 617, 251 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 278, 617, 251 is 1.

HCF(278, 617, 251) = 1

HCF of 278, 617, 251 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 278, 617, 251 is 1.

Highest Common Factor of 278,617,251 using Euclid's algorithm

Highest Common Factor of 278,617,251 is 1

Step 1: Since 617 > 278, we apply the division lemma to 617 and 278, to get

617 = 278 x 2 + 61

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 61 and 278, to get

278 = 61 x 4 + 34

Step 3: We consider the new divisor 61 and the new remainder 34, and apply the division lemma to get

61 = 34 x 1 + 27

We consider the new divisor 34 and the new remainder 27,and apply the division lemma to get

34 = 27 x 1 + 7

We consider the new divisor 27 and the new remainder 7,and apply the division lemma to get

27 = 7 x 3 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 278 and 617 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(27,7) = HCF(34,27) = HCF(61,34) = HCF(278,61) = HCF(617,278) .

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

Step 1: Since 251 > 1, we apply the division lemma to 251 and 1, to get

251 = 1 x 251 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 251 is 1

Notice that 1 = HCF(251,1) .

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Frequently Asked Questions on HCF of 278, 617, 251 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 278, 617, 251?

Answer: HCF of 278, 617, 251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 278, 617, 251 using Euclid's Algorithm?

Answer: For arbitrary numbers 278, 617, 251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.