Highest Common Factor of 784, 309, 278 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 784, 309, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 784, 309, 278 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 784, 309, 278 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 784, 309, 278 is 1.

HCF(784, 309, 278) = 1

HCF of 784, 309, 278 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 784, 309, 278 is 1.

Highest Common Factor of 784,309,278 using Euclid's algorithm

Highest Common Factor of 784,309,278 is 1

Step 1: Since 784 > 309, we apply the division lemma to 784 and 309, to get

784 = 309 x 2 + 166

Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 166 and 309, to get

309 = 166 x 1 + 143

Step 3: We consider the new divisor 166 and the new remainder 143, and apply the division lemma to get

166 = 143 x 1 + 23

We consider the new divisor 143 and the new remainder 23,and apply the division lemma to get

143 = 23 x 6 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 3

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

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 784 and 309 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(143,23) = HCF(166,143) = HCF(309,166) = HCF(784,309) .

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

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

278 = 1 x 278 + 0

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

Notice that 1 = HCF(278,1) .

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Frequently Asked Questions on HCF of 784, 309, 278 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 784, 309, 278?

Answer: HCF of 784, 309, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 784, 309, 278 using Euclid's Algorithm?

Answer: For arbitrary numbers 784, 309, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.