Highest Common Factor of 780, 215, 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 780, 215, 251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 780, 215, 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 780, 215, 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 780, 215, 251 is 1.

HCF(780, 215, 251) = 1

HCF of 780, 215, 251 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 780, 215, 251 is 1.

Highest Common Factor of 780,215,251 using Euclid's algorithm

Highest Common Factor of 780,215,251 is 1

Step 1: Since 780 > 215, we apply the division lemma to 780 and 215, to get

780 = 215 x 3 + 135

Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 135 and 215, to get

215 = 135 x 1 + 80

Step 3: We consider the new divisor 135 and the new remainder 80, and apply the division lemma to get

135 = 80 x 1 + 55

We consider the new divisor 80 and the new remainder 55,and apply the division lemma to get

80 = 55 x 1 + 25

We consider the new divisor 55 and the new remainder 25,and apply the division lemma to get

55 = 25 x 2 + 5

We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 780 and 215 is 5

Notice that 5 = HCF(25,5) = HCF(55,25) = HCF(80,55) = HCF(135,80) = HCF(215,135) = HCF(780,215) .

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

Step 1: Since 251 > 5, we apply the division lemma to 251 and 5, to get

251 = 5 x 50 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, 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 5 and 251 is 1

Notice that 1 = HCF(5,1) = HCF(251,5) .

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Frequently Asked Questions on HCF of 780, 215, 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 780, 215, 251?

Answer: HCF of 780, 215, 251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 780, 215, 251 using Euclid's Algorithm?

Answer: For arbitrary numbers 780, 215, 251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.