Highest Common Factor of 478, 776, 619 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 478, 776, 619 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 478, 776, 619 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 478, 776, 619 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 478, 776, 619 is 1.

HCF(478, 776, 619) = 1

HCF of 478, 776, 619 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 478, 776, 619 is 1.

Highest Common Factor of 478,776,619 using Euclid's algorithm

Highest Common Factor of 478,776,619 is 1

Step 1: Since 776 > 478, we apply the division lemma to 776 and 478, to get

776 = 478 x 1 + 298

Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 298 and 478, to get

478 = 298 x 1 + 180

Step 3: We consider the new divisor 298 and the new remainder 180, and apply the division lemma to get

298 = 180 x 1 + 118

We consider the new divisor 180 and the new remainder 118,and apply the division lemma to get

180 = 118 x 1 + 62

We consider the new divisor 118 and the new remainder 62,and apply the division lemma to get

118 = 62 x 1 + 56

We consider the new divisor 62 and the new remainder 56,and apply the division lemma to get

62 = 56 x 1 + 6

We consider the new divisor 56 and the new remainder 6,and apply the division lemma to get

56 = 6 x 9 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 478 and 776 is 2

Notice that 2 = HCF(6,2) = HCF(56,6) = HCF(62,56) = HCF(118,62) = HCF(180,118) = HCF(298,180) = HCF(478,298) = HCF(776,478) .

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

Step 1: Since 619 > 2, we apply the division lemma to 619 and 2, to get

619 = 2 x 309 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 619 is 1

Notice that 1 = HCF(2,1) = HCF(619,2) .

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Frequently Asked Questions on HCF of 478, 776, 619 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 478, 776, 619?

Answer: HCF of 478, 776, 619 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 478, 776, 619 using Euclid's Algorithm?

Answer: For arbitrary numbers 478, 776, 619 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.